Alright you smart motherfuckers. I just finished The Witness and feel like a fucking genius.
What are some other good puzzle games that makes me feel like Einstein?
>>344164016
Is this a trick? It's 50% right?
La Mulana
It seems like it should be 50% so it probably isn't because this is one of those tricky probability things.
>>344164225
yeah it's 50%
unless there's some bullshit trick we don't know
>>344164016
i think it would be a 5/7 chance it would be gold
2/3
You have 2 possibilities
The other ball is gold
The other ball is silver
That is 1/2, 50%.
1/3
2/3 of the gold balls are paired up with a gold ball.
This is the same thing as the "what is the chance you land 2 crits" question if the first hit is a crit
People will say 1/3 and people will say 1/2
just ignore it
https://en.wikipedia.org/wiki/Bertrand%27s_box_paradox
>>344164225
Yes, unless the other ball turns into a goat.
>>344164016
But I can see into the boxes anon
This is what happens when the picute is more interesting than the question I guess.
Best way I've seen to explain this is Wikipedia:
>The probability that GG would produce a gold coin is 1.
>The probability that SS would produce a gold coin is 0.
>The probability that GS would produce a gold coin is 1/2
>Therefore (probability gold from GG) / (probability gold from any) = 1/1+0.5 = 2/3
Somebody post the Monty Hall problem already
>"paradox theories"
Also known as the "what if logic didn't really exist and we decided to let math take over our life?"
>>344164803
>probability that GS would produce a coin is 1/2
More like 0 cause you already took the gold coin out as part of the premise
>>344164816
fuck you christina
>>344164803
But nigga, it says you already plucked a gold, and asks the probability of what the NEXT ball will be FROM THE SAME BOX, meaning SS box is completely and utterly removed from the equation.
>>344164915
>math isn't logic
>>344164816
depends where you view it from
if you've reached infinity, it's 1; otherwise, <1
>>344164951
>>344165020
This takes into account the probabilities of the boxes you chose. You were MORE likely to pick a box with a gold coin than without one.
>>344164016
If you're into some fantasy shit, you'll probably enjoy something like Legend of Grimrock 1 & 2. Lots of great puzzles and secrets, even if combat is a bit stiff. Sequel is fucking amazing, though.
Currently trying Arx Fatalis and it is turning out to be pretty god damn mind bending at times with how intricate dungeon crawling is.
>>344164016
50% chance.
>>344164803
out of context, as in if someone just get into the middle where you found that the other ball is gold, 1/2 is also correct because the probability of getting gold is literally either yes or no. 2/3 works if you calculate from the start but in the context of the next ball is either silver or gold is 50%, knowing that the other box has no gold balls at all. .
this is a trick puzzle.
>>344165116
It's not asking the probability of you getting two gold coins. It's asking the probability of you getting a gold coin after already taking one out of the box.
Don't overcomplicate things, anon.
>>344164016
It's 2/3.
Since you picked out a gold ball, you can effectively ignore the third box with only silver.
There is twice the chance you picked the first gold ball from the box with two of them, than the box with just one. Therefore, twice the chance the second ball you pick will be gold.
The question is actually asking what the chance is that you randomly chose a gold ball from the double gold ball box. Since there are three possibilities to pull out a gold ball and two of them are in the double box, the probability is 2/3.
If you don't get why its 2/3 probability, it's because if you grab a good coin there's a higher chance is from the box with two gold coins rather than the one with two, so that raises the chances of getting a second gold coin.
>>344164803
>1/1 + 1/2 = 2/3
This has got to be some sort of next level retardation
OP related is 50% because you have already picked a gold and there is a 1/2 chance the next will be gold and 1/2 that it will be silver, 50%, because there are only two boxes you could have picked gold from first, kind of a trick question.
if you disagree you're probably a math teacher and I hate you.
50% chance.
Since you already gotten one gold ball. You can entirely rule out any possibility that you were in the silver/silver box.
Therefore your next puck will either be from the gold/gold box or the gold/silver box. It's a 50% chance your next puck will be gold.
Its 1/2.
Last time it got posted the op tried to argue some other result since the question was "intended to be" a tricky you-dont-really-get-probability question, despite its wording giving you a concrete 1/2.
Anyone who says its not 1/2 is trying to argue from the "spirit" of the question to have some kind of twist you overlooked, rather than the actually really easy and straightforward question actually posed.
>>344164016
https://vladimirslepnev.itch.io/zigzag
>>344165370
But there's a higher chance you got the first ball from the box with two golds.
>>344165505
>the actually really easy and straightforward question actually posed.
You're right, it's really easy and straightforward.
It's 2/3.
>>344165058
It can be logic, but it often flies in the face of common sense because they rely on their own sets of rules. With OP's problem in question, it stands to reason that if you picked up one golden ball, you only have two possibilites left: You chose the box with one golden ball, or the one with two golden balls. But since we're dealing with math logic, they're trying to discover whether or not the odds are 1:2 or 1:3, which is where the paradox comes from.
It's only a paradox because math needs a fucking update.
>>344165370
>>344165461
>>344165505
You aren't taking into account the chances of where you picked the first gold ball from.
This is all en elaborate ruse right? /v/ doesn't actually believe that it's 1/2?
>>344165584
here's why you're wrong
that higher chance doesn't matter because we're not talking about that draw, we're talking about the next one. The chance of the first ball being gold is 100%, the second ball is 50%
>>344164358
>>344164451
>3 in 6 is 50/50
>eliminate 1
>2 in 6 is 50/50
derp
>>344164225
1/3 chance to pick the first box, 1/1 chance to get yellow, we have 1/3 from this
1/3 chance to pick the second box, 1/2 chance to get yellow, 1/6 from this one
1/3 chance to pick the last box, 0 chance to get a yellow
so it's 1/2
>>344165753
>>344165706
>>344165608
>>344165584
the first draw is set you fucking morons there's no chance involved at all
After picking the first ball, there are 2 gold balls and 1 silver ball left. Therefore 2/3 or 66%
>>344165608
>you can only pull one of two coins from your next draw
>the odds of your next draw are 2/3
Not sure if bait or stupid.
50%
>>344165639
Update math, then. Submit a patch that fixes this "bug," because clearly it's not a problem with how you're looking at it.
>>344165639
Math is always updated, it's how far removed our own senses are from pure, unfiltered logic that make it seem like it doesn't make sense.
Math is in fact, more logical than reality.
>>344164016
Try Stephen's Sausage Roll.
>>344165639
>But since we're dealing with math logic, they're trying to discover whether or not the odds are 1:2 or 1:3
The problem with 1:3 is that people are counting balls from another box that they never even touched. Which doesn't make sense. 1/3 takes into account of a box that has two balls left AND the box that has 1 ball left.
If you already taken one ball from the box and pick from the same box, there should be only 1 ball left. So assuming there is 1 ball left in box boxes (because you're picking from the exact same box), the logical answer should be 1:2, which is 50%.
Anyone who says 2/3 is just a retard.
>>344165723
It does matter, because it influences which box you got the ball from,which in turn influences what the second ball is.
>what is the probability that the NEXT DRAW will be
>hurrr its 1/3 because what about the first one too
K Y S
>>344165727
By getting a gold ball, you've eliminated one of the boxes from the equation entirely.
Either you picked the first box and will get the second gold ball, or you picked the second box, and will get the silver ball. So it's 50%.
Is this whole thread retards not understanding the monty hall problem and claiming that math is wrong?
>>344165727
the box with 2 silvers are irrelevant to the question since you already grabbed a golden ball.
so you got it either from the gold/silver or gold/gold box so it's a 50% chance
>>344165837
You're picking from the same box as before you cunt, not from any box. You pick a box, and the first ball you get from it is golden. You do not pick a ball from the other boxes, you're just trying to decide how likely it is that this box will reveal another gold ball. Since only 2 of the three boxes contain gold balls at all, the silver/silver box is discarded since that couldn't possibly be the box we pulled a gold from. Now, the likelihood that this box we've chosen has another gold in it is 50/50, since it can only be one of two boxes.
>>344165824
i read the question wrong moron shut the fuck up or i'll kill you
>>344165838
>Ignoring half of the question in order to make it accomodate your own dull brain
Not sure if bait or braindead.
It's 2/3, you dummies.
We have a single event that resulted in choosing a Gold Ball, and we are determining an outcome caused by the initial event.
To look at it another way, the question is actually "what are the chances you took a gold ball from the box with two gold balls".
>>344165984
It doesn't matter though because you will always pick a gold ball on the first try.
The only thing that matters is the second draw where the chances are 50-50
Anyone who doesnt understand this, read this:
https://en.wikipedia.org/wiki/Monty_Hall_problem
Its not intuitive at first, but its been argued to death.
>>344165753
the box is already picked, the situation is set and you csn completely ignore the 3rd box. it's either the first or second
>>344164016
If it says you've taken a gold ball then it's literally 50/50 right? You have either taken from box 1 or box 2 meaning that one box has another gold and one box has a silver.
>>344165824
>>344165723
The first draw is a gold ball, but where it came from isn't set. The fact that there a higher chance for it to have come from the box with two golds influences the probability of the second draw being gold .
>>344166113
No it isn't, you retard, the question is explicitly "what is the probability of your next draw?"
The first draw is set. It is completely irrelevant at this point except to provide the context that you are dealing with one of the boxes that contains gold balls.
>>344166125
You don't magically always pick a gold ball, that's simply what happened in this event. It could have just as easily been a silver ball.
>>344164016
2/3
If you pick out a gold ball it is either
1.1: The first gold ball in the first box
1.2: The second gold ball in the first box
2: The only gold ball in the second box.
If you picked 1.1, you will pull 1.2 out.
If you picked 1.2, you will pull 1.1 out.
If you picked 2, you will pull a silver out.
All of these three scenarios are equally likely.
Therefore, you have a 2/3 chance of pulling out a gold.
>>344165204
Nigga you're drawing from the same box twice
If you draw one and then someone walks into the room and you ask him to draw the next one from the same box it's not going to change shit
Alternatively if this person chooses another box at random it's a completely different problem
Problem is simpler than it looks. Ignore the third box entirely. If you grab a good ball, there's a 50% chance it's the first one
>>344166165
This is not the Monty Hall problem, the chance is still 2/3 but for different reasons.
>>344166291
>You don't magically always pick a gold ball
You're a retard. Re-read the entire thing. It fucking tells you your first draw was a gold ball.
>>344166175
People seem to be confused and think the first draw matters
>>344166291
>you don't always rescue the princess that's just the storyline
>>344166193
mathematically prove the probability using that logic
>>344166346
A quick read of it might help some of the morons here understand.
>>344164016
0% because I kill myself
>>344166014
>>344166027
I guess I would be better at math if I could read
>>344166165
This is Bertrand's box paradox not Monty Hall. But they're the same in that it brings out the retards in /v/
>>344166094
The question doesnt even begin until halfway through, the first part establishes circumstance and certainty on preliminary factors and therefore entirely discounts them from the equation.
You dont factor a dead set certainty into probability because you're not being asked to predict what has already observably happened, no matter how badlly you want to be the special snowflake that cracked the "real" riddle.
>all these people thinking order doesn't matter
It says the first ball is gold, and it's asking about the next ball picked, so order obviously matters. You either pick up the left gold ball in box one first, the right gold ball in box one first, or the gold ball in box two first.
You then have three possibilities for the second ball respectively: right gold ball in box one, left gold ball in box one, or silver ball in box two. Two of those three choices end with picking up a second gold ball, ergo it is 2/3.
This thread is confirmation that a good chunk of /v/ is retarded. It's 2/3.
100% chance of picking up a gold ball
I'm King Midas
>>344166426
I don't gotta prove it cause some nerd did it 100 years ago.
https://en.wikipedia.org/wiki/Bertrand%27s_box_paradox
>>344166021
Nah, the Monty Hall problem is subtly different. If you want a thread of retards not understanding it you'll have to introduce it separately.
>>344164016
>What are some other good puzzle games that makes me feel like Einstein?
Myst. All of them. Once you graduate those Schizm: Mysterious Journey.
>>344166424
Yes, it's an event that happened, that had a chance to happen, and was more likely to happen if you chose the first box. It is in no way irrelevant.
Let's expand the question to the ludicrous so the issue becomes plain. Same question, except that each box now has 50 balls each, the first box all gold, the second one gold, forty nine silver, and the third box has all silver. You draw a gold ball. What are the chances the next ball you draw is gold? Do you really think it's 1/2?
>>344166294
>If you pick out a gold ball it is either
>1.1: The first gold ball in the first box
>1.2: The second gold ball in the first box
>2: The only gold ball in the second box.
Except there should only be 1 ball left in the first box since you already taken out 1 gold ball in your first draw. And there won't be any gold ball in the second box, just a silver ball since you already taken the gold ball on your first draw.
You either:
1. Take the last gold ball from the first box.
2. Take silver ball from second box.
That's all the choices you have left since you are drawing from the exact same box which should have only 1 ball left. 50% chance is the only correct answer here.
>you arn't taking into account the chance of the first pick
you mean the 100% deffinate gold defined by the question?
not sure if trolling or misapplying logical paradoxes.
>>344166424
Even if you alwyas pick a gold ball the 2/3 chance remains as the question clearly states that the pick is random and therefore the chance to pick the box with two gold balls is twice as much as the box with only one.
>>344166653
>Schizm
>>344164816
Always switch. That's the only correct answer.
>>344166686
>Let's expand the question to the ludicrous so the issue becomes plain. Same question, except that each box now has 50 balls each, the first box all gold, the second one gold, forty nine silver, and the third box has all silver. You draw a gold ball. What are the chances the next ball you draw is gold? Do you really think it's 1/2?
Nailed it.
>>344166165
I think this analogy is wrong because in the OP we're not given the choice of switching our pick. To apply it on the wiki article: If the player picked gate 1 and gate 3 is revealed to be a goat, how's the probability that the player picked the car?
>>344164016
Space chem is a really good puzzle game.
>>344166847
>the probability that GS would be gold is 1/2
you already picked that ball, like I say, misapplying paradoxes.
unless you're putting the ball back in which the question does not specify, in which case I totally understand, but frankly you are a massive troll.
>Everyone saying 50%
Wrong. its 1/216th.
>>344166686
> Same question, except that each box now has 50 balls each, the first box all gold, the second one gold, forty nine silver, and the third box has all silver. You draw a gold ball. What are the chances the next ball you draw is gold? Do you really think it's 1/2?
You're a fucking idiot. Those are entirely different numbers here and of course it won't be 1/2 chance with those numbers. It isn't relevant to OP's question.
>>344164016
English Country Tune and Stephen's Sausage Roll.
I like how this and the Monty Hall Problem can be easily tested in reality, but people make an assumption and vehemently defend it even though it's wrong.
>>344167067
The first draw isn't magic, stop acting like it was. There was a chance for it to happen, and it did. We are now drawing conclusions from something that had a probability of happening.
>>344166723
100% chance that you picked gold, yes. My POINT was to take into account the probability of which box the first pick was from.
If you don't understand this, maybe you should go back to school.
>>344167149
It's literally the same thing as the OP example but with higher numbers to make it easier to understand.
The first pick is random which means there is a higher chance it came from the box with two golden balls. If you say the answer is 50% you're not taking this into account.
It's 2/3.
Since the first ball is ALWAYS gold. You have a 2/3 chance of having picked the first box, and 1/3 chance of having picked the second one.
Therefore the chance of your next ball being gold is 2/3.
>>344166686
Well, you either do or you don't
>>344167149
Fine, then reduce it. We know the numbers are different, but we see that a higher number of gold balls effects the chances of the next draw, so how can the two possibilities be equal in OP's question if there is an unequal number of gold balls in the two boxes?
>>344167149
No, it's actually a perfect example. You didn't get 1/2 because you looked at the numbers. If you did the same thing with OPs question, you would also realize that it's not 1/2.
>>344167231
>>344167218
the probability of an event that has already occured is 100%, what are you spazing out about now? I already get all three ways you think this works. not my fault math is broken.
>>344167231
Since you already taken the first ball which is gold. We can safely get rid of any possibility that it was the silver/silver box. And since you are pulling the next ball from the exact same box... the box should have only 1 ball left in it.
Now imagine this.. There are two boxes.
Box A: 1 gold ball
Box B: 1 silver ball
What are your chances of getting the gold ball? That is the exact question as OPs except simplified for retards like yourself.
>>344166723
You're intentionally failing to take the question at face value to defend your shitty reasoning. Congratulations you're more autistic than the mathematicians that came up with this problem.
>>344164016
>Note you can't see into any of the boxes.
Um, yes I can? There are clearly drawn balls in Ms paint boxes. Don't tell me what I can and can't see bitch, you callin' me blind?
>>344167569
It's not about the probability of the first event.
It's about the effect the first event has on the second. See >>344167369
>>344167358
> It's literally the same thing as the OP example but with higher numbers to make it easier to understand.
It isn't you dumb fuck.
2nd box was 50% gold and 50% silver in OP's question.
Your's was a retarded 2% gold and 98% silver.
You're a fucking retard if you think that's the same shit.
>>344167595
it literally says what is the probability the next ball will be gold, not what is the overall probability of you reaching this outcome
ever heard of a trick question? be mad.
You can test this yourself by drawing the first ball at random, putting it back if it's not gold and resetting the experiment. If it is gold take note of what the second ball was. After some repeats you'll see that about 2/3 of the time you get two golden balls. Use whatever you like for the balls if you're a poorfag.
>>344167716
You completely fail to see his point.
Oh I'm laughin at this thread.
>/v/ argues monty hall
Jesus. Go play Zero escape, maybe then you'll at least understand the basics in a simplified manner.
>there are 6 balls total, 3 gold 3 silver
>one gold was taken out
>now there are 2 golds and 3 silvers still available
>2/5 are gold
>you have a 2/5 chance
>40% chance of gold (2/5), 60% chance of sivler (3/5)
>>344167716
Alright imagine that it's 50 gold, 25/25 gold/silver and 50 silver. you pick one gold there are 74 posible gold balls and 25 possible silver balls. do you still think it's 50/50?
Wait, so if I'm understanding this correctly:
>its 2/3 chance of next coin drawn being gold because of the 3 coins remaining to pull, 2 are gold
Which means anyone saying 2/3 because of "but muh first pick odds" looked up the answer, didn't understand the explanation but still wanted to be a pedantic fuckface?
>>344167830
You're just as stupid as he is.
>>344167716
Not the anon you're replying to, but i'm so lost by your logic it hurts.
Think of it this way. Coin flip
Choice 1 - If heads you win
Choice 2 - If tails you lose.
Now what if you're given another chance afterwards, whats the probability of heads or tails, 50% right?
Is it really 50% after its already been flipped once?
>>344167886
You draw from the same box twice
>>344167886
Fuck, I'm dumb. I didn't see you pick a box and stick with that box. I thought it was pick another ball at random from any box.
>>344167906
>its 2/3 chance of next coin drawn being gold because of the 3 coins remaining to pull, 2 are gold
That's not how it works. Those muh first pick pedantic fuckfaces are right.
>>344165357
Jesus Christ, does it need to be spelled out?
1/(1+0.5)
Surely you could've looked for a few seconds to see what was trying to be expressed.
>>344167768
If you're throwing out the results when the first ball is silver, you will definitely not get 2/3.
>>344164016
TIS-100. You're going to learn the game's own dumbed down version of COBOL if you want to finish it, plus there are secrets in it.
It's right here you morons
https://en.wikipedia.org/wiki/Bertrand%27s_box_paradox
It's 2/3, we have it right here
https://en.wikipedia.org/wiki/Bertrand%27s_box_paradox
The answer is here, Jesus fuck
https://en.wikipedia.org/wiki/Bertrand%27s_box_paradox
Mathematicians have figured it out, you fucking moron
https://en.wikipedia.org/wiki/Bertrand%27s_box_paradox
It's 2/3, Jesus Christ
https://en.wikipedia.org/wiki/Bertrand%27s_box_paradox
>>344168187
Try it. Try it and see.
>>344167369
Another explanation.
There are 3 possible scenarios for your fix pick. While there is a 100% chance of the first ball being gold, you don't know which gold ball you picked. each ball has a 30% chance of having been picked. Think of it as Schrodinger's Box. The outcome of the first pick isn't known and can be either until you grab the second ball.
>>344168089
But thats easily the least plausible explanation in the thread because the question literally makes it impossible to draw from the double silver box.
They dont factor in at all from the point which you are expected to solve and therefore cannot affect probability.
>>344165972
No, 2:3 is a reflection of the fact there are unevenly distributed odds about where your first golden ball came from. It's more likely to be from the box with two than the box with one.
>>344168251
Even unambiguously so. It's not a trick question or a matter of interpretation. The only right answer is unequivocally 2/3.
>>344164016
>I just finished The Witness and feel like a fucking genius.
No you didn't
>>344168401
1/3 chance, not 30%
>>344164016
It's a trick question, just take all the coins and sell them on ebay
>>344167906
This is basic high school probability.
There's some law named after some maths guy that states: WHEN CALCULATING THE PROBABILITY OF X EVEN HAPPENING, JUST LOOK AT ALL THE POSSIBLE CASES, AND DIVIDE THE CASES WHERE X EVENT HAPPENS BY THE TOTAL NUMBER OF CASES.
So, in this case: you've taken a gold ball from a box, which means that there's three possible cases:
1. You took gold ball 1 from the box with the two gold balls.
2. You took gold ball 2 from the box with the two gold balls.
3. You took the gold ball from the box with one gold ball and one silver ball.
NUMBER OF CASES WHERE THE NEXT BALL WILL BE A GOLD BALL: 2
TOTAL NUMBER OF CASES: 3
PROBABILITY OF THE NEXT BALL BEING A GOLD BALL, ACCORDING TO THE THEOREM OF JOHN SMITH THE MATHS GUY: 2/3
ANON'S GRADE IN HIGH SCHOOL: F----
>>344168401
Example 1 and 2 are the exact same damn thing. It's not like the balls are labelled A and B or anything.
>>344168406
2/3 has nothing to do with the silver box. See >>344168401
>>344168406
Maybe the question is a bit unclear but even in a probability course I took last year there were questions stated this way. Its up to the reader to understand that the first pick is also random.
>tfw read wiki explaination
just remembered why I hate math. 100% decided event isn't, imaginary numbers are real, up is down, etc.
carry on.
and the answer according to the question in OP pic related IS 50% and you can fuck off or reword the fucking question.
If /v/ is this finnicky about absolutes, I wonder what they're answer for this is.
A cat is put into a box with a jjar of uranium and a hammer. When the hammer drops, the jar will crack and the radiation will pour out in the form opf poisonous gas, ultimately killing the cat.
I close the box. Is the cat alive or dead?
So this inspired me to put together a shitposting starter pack.
What am I missing?
>>344167906
>the answer isn't the answer because the people saying the answer looked up the answer
>>344168582
They are not the same thing. They are two seperate balls each having their own possibility of having been picked. You can label them if you want to.
>>344168582
It's that mentality that gives you the wrong answer. They aren't the same thing. You can even try this in real life and you'll end up with a 2/3 chance to pick a second gold ball.
>>344168768
Trolley Dilemma, it's not a riddle but people will always argue over it.
>>344168765
Well you fucked and made certain that the hammer drops regardless, so that cat is pretty fucking dead.
>>344168752
nope
>>344168908
What if a miracle happened and the hammer missed the jar? Do you know for sure?
Simplified: 2/3 gold balls are coupled with another gold ball, whereas 1/3 gold balls is coupled with a silver.
>>344168667
>>344168401
Thats pretty concise, thanks for helping me wrap my head around it.
Due to the well-defined subject matter relating to real physical objects I was tempted to argue that this was just math-wank without practical application but when you summarize it like that I can see that you need these rules in place when trying to solve much more abstract problems.
>>344166291
>You don't magically always pick a gold ball
yes you do
>>344164016
So we have two draws, the first of which eliminated a golden ball from the situation.
First we need to determine what could have happened in that first pick.
There's a 1/3rd chance that each box is selected, but only two of the boxes had golden balls. So we can eliminate anything having affected the 3rd box with only silver balls. Either the first or the second box was selected. The chance of drawing a golden ball in the first draw is 100% * 1/3 + 50% * 1/3 + 0% * 1/3 = 1/2. Since we can eliminate the 3rd box as a choice, there is a 2:1 ratio of the golden ball being from 1 or 2, giving us a 2/3rds chance it was from 1 and a 1/3rd chance it was from 2.
So for the 2nd draw we have the following possibilities:
66.6% chance it was this setup:
G
GS
SS
or
33.3% chance it was this setup
GG
S
SS
Now figure out each individual chance to draw a golden ball.
For the box 1 situation the chance is now 100% * 1/3 + 50% * 1/3 + 0% * 1/3 = still 1/2.
For the box 2 situation the chance is now 100% * 1/3 + 0% * 1/3 + 0% * 1/3 = 1/3.
Therefore there is a 66.6% chance you have a 50% chance to draw the 2nd golden ball from situation 1, and there is a 33.3% chance you have a 33.3% chance to draw the 2nd golden ball from situation 2.
(2/3 * 1/2) + (1/3 *1/3) = 4/9
You have a 44.4% chance to get a golden ball the 2nd draw
>>344168878
The answer is to walk away whenever you see trolly tracks that could lead to a moral dilemna
>>344168979
Jesus particles do not cause particles to enter a state of superposition. you killed that cat, brah.
>>344168765
Does the hammer drop?
>>344167890
can you do fractions?
OP's answer is 50% because the only choices left are either the first box, or the 2nd box. And that's after ruling out the third box since the first draw was a gold
Taking 1 gold from the 2nd box in OP's problem would just leave 100% silver left. Therefore you have the first box, which is 100% gold, 2nd box which is 100% silver, keep this part in mind. It's one box with gold for sure or the other box with silver for sure. 50/50 shot it's one box or the other.
Yours is entirely different numbers and won't get 50% because it's a much bigger sample size. If you took 1 gold from the 2nd box, you would then have 24 gold and 25 silver. That is not 100% silver left in the box. 24/49 for gold (48.9%) and 24/49 for silver (51%). It's not a easy clear cut as OP's question.
Your question is a different one than OPs but you're too fucking retarded to understand that.
>>344169057
https://en.wikipedia.org/wiki/Bertrand%27s_box_paradox
>>344169052
https://en.wikipedia.org/wiki/Bertrand%27s_box_paradox
>>344168504
>1. You took gold ball 1 from the box with the two gold balls.
>2. You took gold ball 2 from the box with the two gold balls.
There's no reason to count this twice. There's only 1 gold ball left in the two gold ball box. You either pull the last ball from this box or you pull a silver from the other box. It's as simple as that. 50%
Is Who wants to be a millionaire just a game of luck?
I mean, there's 33.34% chance of being right unless the person happen to know the answer, and lifelines can only get you so far into the game.
Let's say there are 15 questions with 4 choices each. Let's also say there are 3 lifelines: call-a-friend, 50-50, and ask-the-audience.
For each of the 15 questions, there is only 1 correct answer, and 3 incorrect answers, so immediately your chances are 1/3 = 33.34%. You can use each lifeline once. Using phone-a-friend, let's say gives you a 95% chance the person you call is correct. So 1 question is 95%. Similarly, we can say ask-the-audience gives you a 95% chance. Finally, 50-50 will remove 2 wrong answers, so you have 1 right answer and 1 wrong answer, so you basically know the answer. To recap:
Question 1: 33.34%
Question 2: 33.34%
Question 3: 33.34%
Question 4: 95% <--- ask-the-audience
Question 5: 33.34%
Question 6: 33.34%
Question 7: 33.34%
Question 8: 33.34%
Question 9: 95% <--- phone-a-friend
Question 10: 33.34%
Question 11: 33.34%
Question 12: 33.34%
Question 13: 33.34%
Question 14: 33.34%
Question 15: 100% <--- 50-50
Total: 690.08%
Divided by 15 questions = 46.00%
So basically, it's more a less a game of chance, but more than half the people on the show will lose, so it's not very fair. That show is making tons of money off of people.
>>344168401
First and second row is pretty much the exact same shit. There's no need to count it twice.
>>344169296
>>344169165
https://en.wikipedia.org/wiki/Bertrand%27s_box_paradox
>>344169332
>Question 15: 100% <--- 50-50
What
>>344164016
The answer is 2/3 you autistic faggots.
There are three cases in which your first ball is gold
>pick box 1, ball 1
>pick box 1, ball 2
>pick box 2, ball 1
These three events have equal probability. In two out of three, you'll get another gold ball.
>>344169332
>Total: 690.08%
>>344169395
Those two balls are separate entities, so no, they are not the same thing.
>>344169415
Stop counting past events that happened for your probability you dumb fuck.
If we already pulled the first gold ball AND we are pulling from the exact same box, there should only be 1 ball left inside the box we are pulling.
It's either 1 gold ball in box 1. Or 1 silver ball in box 2. Your box paradox shit does not apply to this situation.
>>344169556
https://en.wikipedia.org/wiki/Bertrand%27s_box_paradox
>>344169669
https://en.wikipedia.org/wiki/Bertrand%27s_box_paradox
>>344164016
Rudin - Introduction to Mathematical Analysis is a good game
I'm never sure of how many of the people saying 50% are fucking around or not.
>>344169776
>recommending Rudin
>ever
It's a book only for people who already know their shit.
>>344169746
stop just fucking linking this crap and explain it
>>344169556
>this much effort
>this much autism
>still wrong
Just embarrassing.
>>344169296
>There's no reason to count this twice
There is, because they're two different possibilities. If you've taken one ball out of the box, taking gold ball #1 or gold ball #2 are two completely different events. Obviously, it doesn't matter that both balls share the same color.
Try to imagine this: instead of having gold and silver balls, you have black and colored balls instead.
One box (box A) has a red ball and a green ball, and the other box (box B) has a red ball and a black ball.
If the first ball you took out was a colored ball, what's the probability of the second ball being colored as well?
Surely this time you accept that taking the red ball from box A and taking the green ball from box B are different events?
>>344169746
Fuck you are and wikipedia bullshit. You're a retard trying to apply shit to stuff that has already happened.
>>344169669
And there is twice the chance you pulled the first ball from box 1, since it has two gold balls.
>>344169332
>1 correct answer and 3 incorrect answer
>1/3
That's not how it works anon.
>>344169669
There are two possible boxes you pick on your first choice, but 3 possible balls.
2/3 of them are in the gold only box.
>>344169332
I almost fell for the bait.
Luckily, I'm not THAT stupid.
>>344169891
Sorry about that. Here's a wikipedia article that explains it pretty well;
https://en.wikipedia.org/wiki/Bertrand%27s_box_paradox
>>344169332
>Divided by 15 questions = 46.00%
I like those odds. I'm gonna go play the WWTBAM machine in the local bar until I'm rich.
>>344169993
stop just fucking linking this crap and explain it
>>344169941
Yo, that's cool, it reminds me of a good wikipedia article about a math problem;
https://en.wikipedia.org/wiki/Bertrand%27s_box_paradox
>>344169913
Meant taking the green ball from box A, not B
>>344169913
>There is, because they're two different possibilities
If those gold balls have separate numbers or letters on them, then you would be right, however they are the exact same shit.
It doesn't fucking matter which gold ball was pulled first in the first box.
>>344170079
There are three boxes, each with one drawer on each of two sides. Each drawer contains a coin. One box has a gold coin on each side (GG), one a silver coin on each side (SS), and the other a gold coin on one side and a silver coin on the other (GS). A box is chosen at random, a random drawer is opened, and a gold coin is found inside it. What is the chance of the coin on the other side being gold?
The following reasoning appears to give a probability of
1
/
2
:
Originally, all three boxes were equally likely to be chosen.
The chosen box cannot be box SS.
So it must be box GG or GS.
The two remaining possibilities are equally likely. So the probability that the box is GG, and the other coin is also gold, is
1
/
2
.
The flaw is in the last step. While those two cases were originally equally likely, the fact that you are certain to find a gold coin if you had chosen the GG box, but are only 50% sure of finding a gold coin if you had chosen the GS box, means they are no longer equally likely given that you have found a gold coin. Specifically:
The probability that GG would produce a gold coin is 1.
The probability that SS would produce a gold coin is 0.
The probability that GS would produce a gold coin is
1
/
2
.
Initially GG, SS and GS are equally likely. Therefore, by Bayes rule the conditional probability that the chosen box is GG, given we have observed a gold coin, is:
{\displaystyle \mathrm {\frac {P(see\ gold\mid GG)}{P(see\ gold\mid GG)+P(see\ gold\mid SS)+P(see\ gold\mid GS)}} ={\frac {1}{1+0+{\frac {1}{2}}}}={\frac {2}{3}}} {\displaystyle \mathrm {\frac {P(see\ gold\mid GG)}{P(see\ gold\mid GG)+P(see\ gold\mid SS)+P(see\ gold\mid GS)}} ={\frac {1}{1+0+{\frac {1}{2}}}}={\frac {2}{3}}}
>>344170260
that doesnt explain fuckall
>>344170139
>If those gold balls have separate numbers or letters on them, then you would be right
How would this change the probabilities at all? Writing a number on a ball obviously causes no change.
>>344164016
the answer is zero. you cant take more than one ball because theyre fucking heavy
>>344170260
The correct answer of
2
/
3
can also be obtained as follows:
Originally, all six coins were equally likely to be chosen.
The chosen coin cannot be from drawer S of box GS, or from either drawer of box SS.
So it must come from the G drawer of box GS, or either drawer of box GG.
The three remaining possibilities are equally likely, so the probability that the drawer is from box GG is
2
/
3
.
Alternatively, one can simply note that the chosen box has two coins of the same type
2
/
3
of the time. So, regardless of what kind of coin is in the chosen drawer, the box has two coins of that type
2
/
3
of the time. In other words, the problem is equivalent to asking the question "What is the probability that I will pick a box with two coins of the same color?".
Bertrand's point in constructing this example was to show that merely counting cases is not always proper. Instead, one should sum the probabilities that the cases would produce the observed result; and the two methods are equivalent only if this probability is either 1 or 0 in every case. This condition is correctly applied in the second solution method, but not in the first.
>>344169943
> And there is twice the chance you pulled the first ball from box 1, since it has two gold balls.
It's not asking for the chance of the first gold ball pulled you dumb fuck.
It's asking what are the chances left that the next pull from the exact same box is a gold.
>>344170139
>things are only separate objects if they are labelled so
what a world you live in
Is everyone saying 1/2 pretending to be retarded at this point?
>>344169746
These problems are nothing more than clever wording by fags.
The confusion comes from wording it as "chance of pulling a gold ball" vs "chance of picking the 2 gold ball box"
It's the same with that faggotshit Monty Hall problem:
Instead of saying "door 1" and "door 2" you should say "group of doors 1" and "group of doors 2"
All of these problems are popular because the writers use deceptive phrasing to confuse people.
>>344170290
Shit, sorry man, i'm not very good at explaining things, let me just give you a wikipedia article that does a better job of explaining it than I ever could;
https://en.wikipedia.org/wiki/Bertrand%27s_box_paradox
You should be able to solve this.
>>344170485
is this some new american math bullshit
>>344170424
No problem man, I got a wikipedia article that cuts through the confusion pretty quick;
https://en.wikipedia.org/wiki/Bertrand%27s_box_paradox
>>344170485
Yes it is. 120 = 5!, or 5 factorial.
>>344169971
>There are two possible boxes you pick on your first choice, but 3 possible balls.
>2/3 of them are in the gold only box.
This is not a question where we put 3 balls and to pick from one. It's one where we picked from 2 boxes because we know it was a gold ball we picked.
![screen-shot-2014-08-18-at-10-19-42-am[1].png](https://i.imgur.com/u8GUDSD.png "screen-shot-2014-08-18-at-10-19-42-am[1]")
Let's talk about Achilles and the Tortoise.
>>344170640
nice
ITT: Anon is too retard to read.
>"From the same box"
"From the same box"
>"From the same box"
"From the same box"
>"From the same box"
"From the same box"
>"From the same box"
"From the same box"
>"From the same box"
"From the same box"
>>344170687
Easy, Achiles stepped on a lego before the race and got Achiles heel.
>>344169442
1 wrong answer, 1 right one
1/1=1=100%
>>344170669
There's a couple steps your missing, here, this might fill in your blanks!
https://en.wikipedia.org/wiki/Bertrand%27s_box_paradox
>>344170370
>It's not asking for the chance of the first gold ball pulled you dumb fuck.
I know.
>It's asking what are the chances left that the next pull from the exact same box is a gold.
You already picked a gold ball.
You know that box 1 has two gold balls, while box 2 only has 1.
Therefore, you know that there was double the chance you picked from box one, as opposed to box 2. So, double the chance that your second pick will be gold.
2, fucking, 3rds m8.
>>344170669
2 boxes that have 3 golden balls in them.
Your first ball was gold, so there's a 2/3 chance you picked the first box.
Just picture it as a road with a bunch of forks and it's a bit easier to understand. The main problem is that we don't know where in the road we are. So by looking at all our possible positions and what lies ahead for each of them, we can see that out of 3 possible forks in the road, only 2 of them lead to a second golden ball, ergo, 2/3.
>>344169971
>but 3 possible balls.
irrelevant. Regardless of how many gold balls the first box has, you're still picking from either box 1 or box 2.
You could say box 1 has 100 gold balls while box 2 has 1 gold and 1 silver. But since the only information we have is that the first pick turned out to be a gold ball, it's either the first box or the second box.
Only a idiot would say it was a 101 balls out of 102. Which is basically what all the retards claiming it's 2/3 are saying.
This is assuming you have no idea what were in the boxes. If the first ball picked from a random box is guaranteed gold as the question implies, then the box with silver balls doesn't matter at all; you could only have drawn from a box that actually had a gold ball. After that, "what is the probability of the next ball being gold from the same box" falls to two boxes. The first ball you have drawn doesn't matter at all now. You might as well have drawn a ball from each box because you will only be drawing the 2nd ball from the SAME box as the FIRST BALL. From here only two possible outcomes; you picked from the 1 gold 1 silver box or the 2 gold box. 1/2 is the answer.
>>344171265
I don't know man, Joseph Bertrand isn't really an idiot. He's kind of a cool guy! Here's a Wikipedia article about some of his work;
https://en.wikipedia.org/wiki/Bertrand%27s_box_paradox
>>344171265
>it's either the first box or the second box.
No it isn't, it's either ball 1, 2 or 3. You didn't pick a box. you had a ball chosen for you.
>>344170687
I don't think a race is a very good way to word this. It doesn't make sense to me.
The one about a train that has to stop every time it halves the distance makes more sense.
>>344171272
>The first ball you have drawn doesn't matter at all now.
It does.
>>344171178
This is actually a great way to see it. Basically what the fact that the first ball was golden tells you is that you're in one of the top three paths. Then you're asked what's the probability of the next ball being golden as well, which is just asking how many of these three possible paths lead to a golden ball, with the answer being 2 out of 3.
>>344171420
> You didn't pick a box. you had a ball chosen for you.
If I put two boxes in front of you. Would you pick the left box or the right box?
The only thing you know for sure is that you will somehow pick up a gold ball inside the box you pick. Now tell me the probability you will pick either the left box and the probability of the right box.
>>344172276
You're not picking boxes, you're only checking if the second ball in the box is gold or not.
>>344171582
Only in regards that it is gold but that is a given. The box you draw it from only has 1 ball left and only 2 boxes have a possibility of a gold ball. Thus you only have a 50% chance, out of the boxes that had a gold ball, for the 2nd ball to be another gold ball instead of a silver ball.
>>344172426
Here's a wikipedia article that explains why you are wrong.
https://en.wikipedia.org/wiki/Bertrand%27s_box_paradox
>>344172426
But there are three possible "first draws" that are gold. Two of which result in a guaranteed second draw of gold, and one that does not.
>>344172276
I put two zips in front of you, what are the odds you unzip my dick
>>344172426
If you picked the box with two gold balls you could have pulled gold ball number 1 or gold ball number 2 with equal probabilities.
Just read that wikipedia article.
>>344172276
The odds would be 50% to have picked a given box if you could have picked the silver ball, in which case the odds would be 2/4. But in this scenario, the silver ball could not have been picked, and thus the likelihood of having picked the second box can't stay the same either.
How can ANYONE say it's not 50%.
The fact you got gold means the third box is ruled out. The next ball you draw is either gold or silver. It's 50%.
>>344172918
Consider this case:
Box 1 has 100 gold balls.
Box 2 has 99 silver and 1 gold ball.
Is the probability still 1/2 for you?
>>344172918
>Hi guys I just got here and haven't read any of the thread
>>344172918
Because it's been mathematically verified to be 2/3.
>>344166014
Except the likelihood that you picked a gold ball from the box with two gold balls is higher.
Imagine if you completely discount the silver box. In that case your distribution is as follows.
2 golds vs 1:1. And we know you got a gold. As such there are 3 possible targets. 1/3 to pick gold a from box 1, 1 /3 to pick gold b from box 1 and 1/3 to pick gold from box 2.
As such your chance of picking the two gold box is 2/3 as you were more likely to have picked from the two gold box in the first place.
>>344172918
I don't know man, mathematicians have been pretty dead set on the fact that it's 2/3.
Here's a wiki article on that subject;
https://en.wikipedia.org/wiki/Bertrand%27s_box_paradox
>>344172918
There's 2 gold balls in box 1
There's 1 gold ball in box 2
So, double the chance the first pick is from box 1.
If you pick a ball from 1, that means the second will be gold
If you pick a ball from 2, that means silver will be the second.
As already established, there is double the chance the first gold ball picked was from box 1, therefore, 66% chance that the second is gold, vs 33% that the second is silver.
Lets change the nature of the problem. Lets change it to
what is the chance of pulling out the same colored ball twice in a row from the same box? Ignore gold, ignore silver. The raw answer is 50 percent. The probabilities of this problem do not go up or down upon recieving either color of ball and instead stays 50 percent forever. Prove me wrong.
>>344173181
I ain't reading all that shit nigga
>>344173163
That would change the entire case. You can't just add more balls, that's gay.
>>344173239
>>344173249
This is severe over thinking. You pick a ball. It's either gold or silver. It doesn't matter if I picked gold ball A B or C.
>>344173545
I don't know man, overthinking isn't really a thing in math. Math simply is.
Here's a wikipedia article explaining what I mean;
https://en.wikipedia.org/wiki/Bertrand%27s_box_paradox
>>344172591
The flaw in the wikipedia logic is that they add everything. It doesn't make sense to anyone who actually knows logic and reasoning of the question.
And please don't say just because it was on wikipedia means it has to be true. Wikipedia is full of shit most of the time due to some retarded bias owner of the page.
Bertrand's box paradox is wrong as fuck. He's just as stupid as anyone who said the answer is 2/3. That I can guarantee. Bertrand is a fool. Probably really bad at gambling as well.
Can mods just delete this thread.
>You pick a ball.
You don't pick a ball. The ball was already picked for you. You're only checking what colour the next one is.
>what is the probability this happens
>you picked gold, but it still matters how you picked it and the question is totally not a trick question or badly phrased
>look, wikipedia agrees with me
science...
whats next, you gunna tell me 0 is not equal to 1, despite that being proved by math? 0=2 aswell if that didn't trigger you.
>>344173773
Meant for. >>344173545
>>344172890
But you're not picking the balls inside the box. You know for sure you whichever box you pick, you will grab a gold inside the box. So what you are actually picking isn't the balls inside the box, it's the box itself.
>>344165753
Thank you, Tolkein.
>>344173902
>But you're not picking the balls inside the box
Correct, you're not picking anything. A gold ball was picked for you, which has a 2/3 chance of being from the first box.
>>344172591
>>344172619
>>344172784
Except it's not making sense to me. The problem in the OP says outright that the first ball you draw is gold AND that you will only draw the second ball from the same damn box and it's asking what are the chances the SECOND ball will be gold. You can toss the first ball now that you know it's gold, it should be out of the equation completely because for this problem, the first ball is a 100% chance of being gold. That completely rules out the two silver box and leaves only a 50% chance of you having picked the box with 2 gold or 1 gold 1 silver.
>>344174097
If you picked a gold ball from box 1, which ball did you pick?
>>344173874
Yeah I know, but it's still 50%.
The next ball is either gold or silver. There's no deep probability problem here.
>>344171178
Well done anon, this is the best way to explain it.
>>344172102
Fuck off with your aleph number shit.
>>344174283
No, the next ball is either gold, gold or silver.
>>344174272
Why does that matter? You don't need to label them. That makes so little sense.
>>344173719
>Bertrand's box paradox is wrong as fuck. He's just as stupid as anyone who said the answer is 2/3. That I can guarantee. Bertrand is a fool. Probably really bad at gambling as well.
Kek, okay anon.
>>344174283
>The next ball is either gold or silver.
Incorrect. The next ball is either gold, gold or silver.
>>344164016
Get the Talos Principle of you want good puzzle game. Very hard but really rewarding
>>344171178
this is bullshit though. youve taken a gold ball out, so there are only two possibilities: GG or GS. It's 50%, this is not Monty Hall.
>>344173545
It does you retard, because gold balls A and B are in the same box as each other and gold ball C is in there with a silver ball.
>>344174395
No, the next ball is either gold or silver. There's not some third box that also had 2 gold balls in it.
>>344164016
Ugh, mods need to start banning this picture as an op. This is the fifth day straight i've seen a new thread with this as the op asking about "video games with puzzles" intending to start a shit flinging war between idiots. It has worked 100% of the time, and gets well over 300 posts.
This isn't about video games. This is cancer
>>344174395
>>344174483
I get the reasoning but that's overthinking it. Don't label and it's 50%
>>344174675
>Hey anon randomly pick a slice of pizza, 7 of that are smeared with shit and one has pepperoni
>You can either pick shit or pepperoni so it's a 50/50 chance
>>344174705
But they're already labeled gold or silver.
>>344174705
It's not overthinking it, it's just how it is.
The first box has two gold balls, both of which could be the one you picked.
>>344174689
Beats console war threads. Since when has /v/ been on topic anyway.
>>344173523
with the original preface? 66%. your distribution is a:a a:b b:b
With the wording of your question, nothing changes after the initial draw so the initial probability remains the same.
The original question though has a different wording which changes the dataset. (which also makes it 66% but that's a different thing)
>>344174483
Are you guys trying really hard to ruse the good faggots of 4chan, because there are 3 boxes, two of which have at least 1 gold and one of which with no gold. You drew a gold and there is only one ball left in the box. It can only be gold, or silver.
Replicate this problem yourself using jellybeans or something in your house. it will be 50 percent.
>>344173243
It doesn't matter if the chance of your first ball being gold is higher if the base state is "Your first ball is a gold ball". The question isn't "What's the chance of first taking a gold ball and then getting another one?"; it's "You have already taken a gold ball. What is the chance of getting another one from the same box?".
>>344174823
So this is what it's like to try and argue with someone from tumblr. They just throw logic out the window and start flinging shit.
>>344175028
Yeah dude we set up this wiki page and countless other websites detailing the problem just to troll /v/
>>344174839
Yes but that doesn't matter. If I have box A, there is a 100% chance the next ball is gold. If I have box B, there is 0% chance the next one is gold. I do not know which box I have.
>>344174705
So if you replicated this irl, would it be 2/3 if you write A, B, and C on the gold balls and 1/2 if you don't?
The fact that you don't know which gold ball you picked doesn't mean it won't change the numbers behind the problem.
>>344174097
>The problem in the OP says outright that the first ball you draw is gold
That's the fucking point. You KNOW you drew gold, and you know that one box has two gold, and the other has 1. Considering that the first box has 2 gold and the second has just one, what are the chances of where you drew the FIRST gold ball. 2/3 for box one, and 1/3 for box two. 2/3 is the answer of the question, since if you drew from box 1, you KNOW you will get another gold ball, and if you drew from box 2, you KNOW you will get silver.
>>344173902
But if you picked the box with a gold and silver ball and then drew out the silver, that draw is no longer valid to the proportion since the constant is that the ball drawn was gold. It's because of that the proportion is reduced from 2/4 to have picked a given box to 2/3.
In case this is your misconception, the question isn't stating that if you were to try this experiment at home that for the sake of the thought experiment you're guaranteed to draw the gold ball from the gold-silver box. It's only asking: IF your first pick was gold, THEN what are the odds the other ball in the box is also gold.
>>344171178
Your not changing the box you are choosing from, therefore you are not choosing a ball, but a box.
Which box are you in?
>>344174705
They're two different gold balls you dolt. Just because you think they're interchangeable doesn't mean there aren't still two balls in there you could choose.
>durr it's a trick!
no it's not
You picked one of two boxes (GG, GS) because we're told you pulled out a gold ball. Of the boxes that it was possible for you to pick (which SS is not one) one of two will result in a second gold ball. In the case presented there is no ambiguity, it's just 50/50.
>>344175139
The base state says you have a gold ball but doesn't say which of the three gold balls it is.
>>344175279
Box 1 has a and b.
Box 2 has c and d.
I pick a gold one.
My first pick is either (a, b) or c.
The next one is (b, a) or d.
You are right in saying you can label them. But you cannot treat the ones in box 1 as multiple cases.
I'll use as an example 900 times where you grab a ball from a random box.
300 times you will pick the GG box.
300 times you will pick the GS box.
300 times you will pick the SS box.
Out of the 300 times you pick the GS box, you will grab the gold ball 150 times.
So 300 times grabbing a gold ball from the GG box plus 150 times grabbing a gold ball from the GS box means 450 times you will be faced with this dilemma (which is 1/2).
Out of those 450 times, 2/3 of them will give you another golden ball and 1/3 of them will give you a silver ball.
But the problem is the wording of the question, because it's not completely clear what is relevant to it. You should avoid saying something like 'you take a ball from a box at random' and then follow it with 'it's a gold ball.' It should be worded:
>In the situations where grabbing a ball from a random box nets you a golden ball, what is the chance of getting another golden ball from the same box?
That clearly gives you the 2/3.
The way the question is worded in the OP makes it sound like you can reduce the question to two boxes and then getting the 1/2.
>>344175490
Except you picked that first ball at random, so it's more likely to have come from the GG box.
>>344175336
>what are the chances of where you drew the FIRST gold ball.
The probability of that event has collapsed, you already picked up the first gold ball. It's totally irrelevant to the established time frame.
Yes, probabilities change over time as new information is available.
>>344175490
But since GG has two gold balls, while GS has one, there is double the chance that the first pick is from GG. That is where everyone is getting 2/3s from, and they are correct.
>>344175336
You are OVERCOMPLICATING it. If you drew a gold. that leaves two possibilities, box 1 or box 2. Box 1 has a one hundred percent chance of an additional gold while box 2 has a zero percent chance. There are only those two boxes, and you dont know which. Ergo you have a fifty percent chance of it being gold.
>>344174097
Your scenario:
>I have a gold ball
>1st box has another gold ball
>2nd box has a silver ball
>probability of picking the box with gold ball?
>1/2
And that is true if this is the wording of the problem.
But we are dealing with different problem.
Our scenario:
>step 1: I pick a box and pull a ball
>step 2: Is the ball gold? If yes, go to next step; if no, go to step 1
>pull the next ball from the same box
>probability of gold ball?
>2/3
In this wording we know what happened in the past. We know that it was more likely that the 1st ball was pulled from the box with 2 gold balls.
This is why people struggle with this and Monty Hall problems.
>>344175669
No it isn't irrelevant you complete retard. Do you think ambiguity about past events is impossible? If I fucked your mother last night you wouldn't necessarily know about it, right? So why is it so hard to grasp that you don't know which gold ball it was you took from the box?
>>344175636
>In the situations where grabbing a ball from a random box nets you a golden ball, what is the chance of getting another golden ball from the same box?
>That clearly gives you the 2/3.
You're retarded.
You picked up the gold ball or are in a situation where you randomly picked up a gold ball. The chances of picking a gold ball at that point is irrelevant (technically it's 100%)
Go back to school.
The wording will really fuck someone up.
>>344167853
>Play that segment
>The thingy is in the first box I chose
Anyone else /unlucky/?
>>344175660
>Except you picked that first ball at random, so it's more likely to have come from the GG box.
That's not how probability works. It is not past-facing.
If the problem is "you picked a box and then picked a ball and it was gold, what are the chances the other ball is gold," then the chances of picking a box with at least one gold is 100% and the chances of picking the gold out is 100% even if you chose the GS box.
Events that have already occurred are no longer probabilistic, they are determined.
I'll repeat that
EVENTS THAT HAVE ALREADY OCCURRED ARE NO LONGER PROBABILISTIC, THEY ARE DETERMINED
>>344175759
You are adding steps. You have a gold ball from box one or two. That is your starting info.
>>344175996
>EVENTS THAT HAVE ALREADY OCCURRED ARE NO LONGER PROBABILISTIC, THEY ARE DETERMINED
Except that you don't know what happened.
You only know you have a gold ball, you don't know which one.
>>344175336
BECAUSE the first ball is gold no matter what, that ball shouldn't matter in the equation because it can't be drawn again. Either gold ball in the GG box can be substituted for one another and nowhere does it say otherwise.
>>344175702
Holy fuck, you're retarded.
>There are only those two boxes, and you dont know which.
Okay, fine, a different angle since you clearly don't get it. You drew a fucking gold. There's two gold in box A, and one in box B. If you had to bet money on which one you drew gold from, which box would you pick?
I think its clear now that the wording of this box paradox is 100% fucked up and needs redoing.
thats as much of this as i'm willing to entertain.
>>344173249
>https://en.wikipedia.org/wiki/Bertrand%27s_box_paradox
The only reason these mathematicians come up with this shit is to circlejerk over how much smarter they are than everybody else but the problem, as stated, does not function that way. We have already picked a box and it has a gold ball in it. Probability of the picking that first gold ball is no longer taken into account because the problem states we have already picked it. We have a box with 1 confirmed gold ball in it and we're not reaching into any of the other boxes so we know, for a fact, that we did not get the SS box. That means, we have the GG or the GS box. It doesn't matter that there is a 0% chance of picking gold from the SS box or any of that shit because we know that it is now either the GG or the GS box, therefore, it is a 50/50 chance. It's like these people have never heard of Occam's Razor.
I'm kinda glad I'm so stupid if this is what smart people do all the time.
Why do retards who know literally nothing about math or probability try to argue like they know what they're talking about?
>>344176143
That's not the question. Fuck.
>>344175816
>No it isn't irrelevant
Yes. Yes it is. For the stated problem (and the dumbass restatements) the chances of having picked a gold ball as your first ball are 100% because it ALREADY FUCKING HAPPENED
>>344175636
Except that's an inaccurate model. Let's incorporate selection order into the nomenclature by saying that GS and SG are the same box, but the first letter is the ball that was picked first.
All together, disregarding the information we know about which ball was chosen, these are the possibilities:
GG
SG
GS
SS
Add in what we know (that gold was chosen first) and you can eliminate SG and SS
This leaves you with GG and GS, a 50/50 split.
All of you should kill yourselves, this is not difficult in any way.
>>344175996
You can still use probabilities to describe events that have happened but about which you don't have information. If you're going to be that stupid you might as well say the gold or silver ball in the box is already in there so it's only a 100% or 0% chance of finding one.
>>344176341
/thread
>>344175826
In my example you would reach a 450 pool of situations out of which 2/3 are GG and 1/3 are GS. How do you reach a different pool of situations?
>>344164016
How exactly am I supposed to interpret questions like this? If I assume that you pick another ball at random whenever you pick a non-gold ball, then the chance of drawing a second gold ball after the first is 66%. But if the experiment is only being done once and you already have a gold ball in your hand, then the probabilities beforehand are irrelevant are irrelevant and the probability is 50%. What indicates which of these scenarios the question is asking?
>>344176341
>We have already picked a box
NO YOU HAVEN'T
NO BOX WAS PICKED, ONLY A BALL
SINCE THERE ARE 2 GOLD BALLS IN BOX A AND ONLY 1 IN BOX B THERE IS A 2/3 CHANCE THE BALL YOU HAVE IS FROM BOX A
>>344175139
That's the thing - your probability is dependant on the base rate still.
Take it this way imagine you take the gold you are holding out of the equation, you're left with 3 balls.
1 silver and 2 gold distributed randomly. The ball in your box can be any of these 3. The chance of of you picking up a silver next is only 33%.
>>344176143
Thats gambling or a gameshow. If you were to recreate this event one hundred times in a row it would likely be fifty or close to fifty percent. There is no info besides whats show. It is fifty percent.
>>344176394
It is the question though.
>>344175596
Why can't the balls in box 1 be treated as multiple cases? There are multiple balls in it.
Regardless of whether you care about which one you draw or not, you will still have two possibilities for box 1: drawing A or drawing B.
You shouldn't ignore numbers in the equation just because they don't feel right.
In real life, the balls would be distinct and you wouldn't know which one you picked from which box. So every possible gold ball is fair game.
There are clearly only two possibilities.
1) You understand statistics enough to be outraged at wrong answers.
or
2) You understand statistics enough to troll the others.
>>344176051
I'm not adding steps. The problems states that at step 2 the answer is yes.
The fact that the answer was "yes" is crucial which gives us probability 2/3. The gold ball isn't handed to you by god.
If latter is the case then the answer would indeed be 1/2.
>>344176471
Huh
that's not the question. The question isn't what the chance dor the first one was. The quest is what is the chance the next ball is gold. The first ball is already out of the equation.
>>344166585
>>344166613
>Actual retards who think they are smart.
It's 50%. the first ball is gold meaning box 3 is irrelevant. You've either:
>Reached into box 1 and will get another gold
>Reached into box 2 and will get the silver
>>344164016
It's 50%
There are three boxes - The one you just picked has one gold ball in it. That narrows it down to two boxes. You have either picked the gold ball box or gold/silver ball box.
>>344176496
go do it
right now
post results so we can all see how wrong you are
>>344176471
>NO BOX WAS PICKED, ONLY A BALL
See >>344164016
>You PICK A BOX at random.
You see? The problem states we have picked a box, we reached in, and pulled out a gold ball.
>>344176471
You fucking moron, you pick a ball from a box and it happens to be gold. Therefore you have picked a box from which the gold ball came because the box had the damn ball in it.
>>344176641
>The first ball is already out of the equation.
No it isn't. The first ball decides what the next one will be.
>>344176091
>that ball shouldn't matter in the equation because it can't be drawn again.
Except it does, because the fact that you drew a gold on your first pick, means you can infer the most likely box that ball came from, which is box A, since it has two gold balls, while B only has one.
It's pretty simple really. If you asked:
>"What is the probability that we select a box and it has 2 golden balls in it?"
It's clearly 1/3rd.
But what they're asking is:
>"What is the probability that we selected a box and drew one golden ball, and then from the same box pulled the second ball out and it is golden as well?"
There are 6 possible first draws, [G G] [G S] [S S]. Since you know that you drew G first, the remaining possible picks are G, G, and S from the first two boxes. Therefore you have a 2/3rd chance to get G on the second pick if you start only from the selection of scenarios in which G was first chosen.
>>344176396
>This leaves you with GG and GS, a 50/50 split.
Correct, like I said 450 situations out of the initial 900 (which is 1/2).
Out of which 300 are GG and 150 are GS. 2/3 and 1/3.
>>344176396
There's G1G2 and G2G1 idiot
People are pretending like the question only says you pick G1 first.
>>344176437
because the idea of having randomly selected one of three boxes has already gone out the window. You did not pick the SS box. The chances of picking the SS box are effectively 0%.
>>344176084
>except you don't know what happened
You know that you picked either GG or GS, and that the chances of having picked SS are actually 0%, because we've established that you chose a gold ball.
If the problem presented were "what are the chances of selecting two of the same color ball" the answer would be 2/3s, but that's not the problem presented. Declaring that a box with at least one gold ball was chosen changes the probabilities.
>>344176592
I don't know how to word it right.
Could someone help me out on this?
What I mean to say is that if I picked a in box 1 the next one is automatically b. If I picked b the next one is automatically a. They're interchangeable. That is one case. The other case is box 2.
>>344176471
Why? You're either picking the box with GS or GG. You already picked out the gold ball at a 100%. Maybe if the question was phrased differently, but in the context of the question it's a 50%.
>>344176483
Yeah, I thought about it more after reading the wiki page and can easily see how it's 2/3.
my issue with this, though, is that rather than other mathematical paradoxes, this feels little more than an attempt to trick the reader into focusing on the wrong point, though, and as such ends up feels cheap.
>>344176678
Again, you aren't taking into account of which box the first ball came from.
2/3 has nothing to do with box 3.
You call me a retard, yet you clearly have no idea what you're talking about.
>>344176851
>because the idea of having randomly selected one of three boxes has already gone out the window. You did not pick the SS box. The chances of picking the SS box are effectively 0%.
But it does not take into account the SS box. It considers the 450 situations where you get a golden ball.
I'd agree with you 1/2 guys if the question was worded differently, and even said it should be clearer.
The question can literally be dumbed down to
>There are two boxes infront of you, one has a gold ball in it and one has a silver ball in it. What are the chances of picking the one with the gold ball?
Can't believe there are clowns arguing over this
>>344176740
this one is super evil, since it's correct.
>>344176960
>This feels little more than an attempt to trick the reader into focusing on the wrong point, though, and as such ends up feels cheap.
This is true.
t. mathematician
>>344176787
No, it's not an if/and question.
Pick a gold ball out of the boxes 1500 times out of 3000
1000 times it came from the box with 2 gold, 500 times it came from the box with 1 gold
You pick a gold ball again. Do you think it was more likely you pulled it from the single-gold box, or the double-gold box?
>>344176609
There are only two steps. Recieve ball, then deduce box. There is nothing else. The first ball is gold. This eliminates box 3. Without more info. you know that of the two boxes remaining, one has two gold and one is split, and you have a gold now. Meaning of this box you have, the next ball you pull will be either gold or silver in equal likeliness, because that is the only info given to you. You are given a gold ball from this problem, meaning the two boxes are gg or gs. You already have a g, so the next ball will be g or s. Thats it. The question implies your first pick will always be g, there is no need for more info than that.
>>344177137
Doesn't change anything. You can add infinite boxes with 2+ silver balls in it, we still know we started with picking a box that had 1 gold in it.
>>344177137
2/3
Since the first ball you draw is gold, that eliminates the possibility of you drawing from the 3rd box first.
Which means the box you draw from again either has 1 silver or 1 gold ball in it.
50%
You don't even need to know anything about statistics and probability to figure this out.
>>344177137
Fifty percent. Twentyseven boxes were already eliminated.
>>344177137
2/3 of the gold balls are paired up with a gold ball.
>>344176601
>statistics
Anon...
>>344176787
you're treating the [g,g] box as though you haven't picked a gold already, the probability of balls left boils down to a gold or a silver.
>>344177271
You do need to know something about statistics or probability to get the right answer, though.
>>344177137
The answer ismuh dick
>>344177308
The question implies your first pick will always be gold without fail. 50 percent.
>>344177163
Except the question states the first box was picked at random. The odds of it coming from box 1 are twice as high as it coming from box 2.
>>344177395
Are you saying 50% isn't right or...?
>>344177354
If you take a statistics class, you'll learn a lot about probability.
>>344176972
The ball being right or left doesn't matter. You have taken the ball already, this part of the math doesn't matter.
You have a gold ball in your hand, and it's a 50/50 whether or not that ball is from box 1 or box 2.
>>344177225
Badly worded - that had at least one gold ball in it.
>>344177137
Let's say you grab a box at random 2700 times. 100 times each box.
2500 times you get silver balls from SS boxes.
100 times you get golden balls from GG box.
50 times you get golden balls from GS box.
50 times you get silver balls from GS box.
Since you only consider the cases where you get golden balls, that's 150 situations, where there's a 2/3 chance of getting the GG box.
>>344177163
>Recieve ball, then deduce box.
>the next ball you pull will be either gold or silver in equal likeliness
So close, but wrong. One box has 2 gold, while the other has 1. You know this. Which box did you pull the first gold from most likely?
>>344177163
You don't receive the ball - you pick it from the box. And you picked it from the box with 2 gold balls with 2/3 chance.
>>344177481
No it doesn't. It says you picked a ball at random and it happened to be golden.
>>344177531
No it isn't. You could have reached into box 2 and picked out a silver, too, the question just notes that it didn't happen this time.
>>344177308
A gold ball has been removed. There are either 0 or 1 pairs of gold balls. The answer is 50%
There are 6 possible ways to pick out balls based on the OP's configuration.
I have a 1/3rd chance to pick any given box.
1. I pick Box 1's Golden Ball 1 and then pick Box 1's Golden Ball 2.
2. I pick Box 1's Golden Ball 2 and then pick Box 1's Golden Ball 1.
3. I pick Box 2's Golden Ball 1 and then pick Box 2's Silver Ball 2.
4. I pick Box 2's Silver Ball 2 and then pick Box 2's Silver Ball 1.
5. I pick Box 3's Silver ball 1 and then pick Box 3's Silver Ball 2.
6. I pick Box 3's Silver Ball 2 and then pick Box 3's Silver Ball 1.
If you state that a Golden Ball was picked first, then situations 4, 5, and 6 are not possible situations. Therefore you are equally likely to pick situation 1, 2, or 3, and the first 2 give you the desired result.
The answer is 2/3. It's plain as day.
>>344177504
The first box was random but the ball was gold. Consider the fact that there are about 50 anons in this thread, and we all now have a gold ball as our first ball.
ITT: People who know a little about probability, and people who do not.
>>344177642
sorry, #4's second pick should real Golden Ball 1
>>344177504
Except if the question says "you pick a gold ball", the odds of you picking a gold ball are 100%, meaning you can eliminate that probability.
>>344177037
It actually can't, since the right question is.
There are two boxes in front of you, one has two gold balls, the other a gold and silver. You picked up a gold ball, which box is more likely to be the source.
>>344177705
That doesn't matter when it's a hypothetical.
>>344177531
>The ball being right or left doesn't matter.
I never said this.
>it's a 50/50 whether or not that ball is from box 1 or box 2.
No, it isn't, this is where you are wrong. Box 1 has 2 gold balls, while box 2 has just one. Which box did you pull the first gold from most likely?
>>344177581
But the first ball is always gold, there is no chance of this. If we chose box one or two, the first ball we pick out will be A gold or THE gold. That is the fact of this problem.
>>344177770
No, the question says you pick a ball and it happens to be gold.
>>344177770
>2/3+1/3=1
stop the fucking presses
>>344177481
>>344177635
I could've picked the left or right gold ball in box 25 first, or the lone gold ball in box 26 first.
There are 3 possibilities:
G1G2
G2G1
G3S49
Two of these end with picking a second gold ball.
>>344164016
This question is intentionally vague. It doesnt tell us FROM WHERE it wants us to calculate the probability.
The probability of being able to get two gold balls is 33%. This is a FACT.
However you've already got one Gold ball. This means that we start the probability over from this point. There is a 50% chance that you got the 2 gold ball box, if you already have one gold ball since there's only two boxes where you can get two gold balls.
"Why isn't this like the monty hall problem, where your chances are boosted above 50%??"
Visualize ten thousand doors. You pick one and then are asked, forget what you picked, do you think you were wrong or right? Obviously the odds of you picking the right door is 1 in 10,000 so the chance of you having been wrong is absurd. The monty hall problem is the same thing. The odds of you having been initially wrong are 66% meaning you get a 66% chance if you swap because you are in essence now wagering your initial choice was wrong.
This bares ZERO RELEVANCE in this case. You already picked and got a gold ball, you don't get to switch boxes now.
TL:DR
The probability of being able to get two gold balls in this set is 33%.
The probability of drawing a second gold ball, considering you already have one is 50%.
>>344177887
probability of picking a box =/= probability of picking a ball
I don't know if people are reading the question wrong or what, but you pick again from the SAME box. Which mean since you drew from a box and, 100%, picked a gold ball, you COULD NOT have picked from box 3. Meaning there's only two boxes left, one with a single gold ball and one with a single silver ball.
Fifty percent.
>>344177896
No it says you pick a random box and get a gold. All other info is conjecture.
>>344176907
In the problem you don't know which ball or box you picked.
A -> B and B->A both result in the same outcome, but they have different inputs. That would make them different cases since they're different possible scenarios.
If you threw one of those scenarios out of the calculation, that would mathematically mean it CAN'T happen. Which obviously isn't the case. There are two balls and either one can be used as an input for the scenario, so two cases for box 1 must exist.
What does the probability matter when there's no choice involved in the problem? Even if you added a step to choose a different box, you wouldn't since you already have at least one gold. You might as well get rid of the double silver box as well, because the problem basically discredits its existence.
Just pull out the other ball and be done with it. This question is dumb and pointless.
>>344178043
If you picked from box 1, which gold ball was it, the left or right?
>>344178037
Since your first ball will be gold, its the same thing as a matter of fact.
>>344178043
>>344178010
Please refer to here >>344177642
There are 6 possible ways to draw 2 balls. 3 of them are no longer possible if you state that we first drew a gold ball. There are 3 remaining possibilities and 2 of them have a golden ball drawn 2nd. The answer is 2/3rds.
>>344178010
/thread
>>344177886
>Which box did you pull the first gold from most likely?
Doesn't matter. Refer to this anon.
>>344175996
>>344177938
>Sarcastically acting like simple maths is hard
>In this thread
>>344178190
Left or right is irrelevant. You are guarenteed a gold ball. Thepis question eliminates the possibility of getting a silver ball first.
>>344164016
The wording of the problem is deliberately muddling it to make it look like the answer should be 1/2.
Think of it like this instead and it makes more sense why the answer is actually 1/3.
>>344178010
>There is a 50% chance that you got the 2 gold ball box, if you already have one gold ball since there's only two boxes where you can get two gold balls.
Wrong. Box 1 has 2 gold balls, while box 2 has just one. Which box did you pull the first gold from most likely?
I've simplified the wording for everyone who seems to think it's 2/3s.
>>344177626
And the question proceeds from that point, you dungus
>>344178386
*2/3
>>344178043
Again - you're not picking boxes but ball.
a) picking up a box with two gold balls in situation GG GS = 50%
b) picking up a second gold ball after you have picked up the first in situation GG GS = 66% As the first gold ball you have picked up is either
G1 > which is tied to g2
G2 > which is tied to g1
G3 > which is tied to s
>>344178386
That is also 50%.
Your first two cases are the same outcome. It's interchangeable.
There's 3 golds you could have picked
2 of those 3 golds are paired, so its clearly 2/3
>>344178496
Yes, and?
>>344178451
You changed the problem by removing the conditional probability element that you have so much trouble understanding.
The question asks what your chance of getting a gold ball is, if you already had confirmed one gold ball from before.
>Know first ball you got is gold
>Odds out silver only box
>One box has 2 gold, one has 1 gold and 1 silver
>Since you get one gold ball, you can ignore one gold ball from both, since you don't know which box you chose, but know you have a gold ball.
>What remains is one box where the second ball is silver, and another where the second ball is gold
1/2
>>344178418
The first grab is guarenteed a golden ball, so it doesnt matter.
The question might as well be saying you chose the left ball, since both boxes have the left as gold. It eliminates box three and guarentees the first pull is gold. Stop overanalyzing, the first ball is gold. All over info is LITERALLY irrelevant.
>>344178592
Nothing is removed, this is simply what will happen next. Jesus.
>>344178451
Sure, if you think that every time you pick a ball from the GS box you will get a gold ball first.
Ok people, answer me this one.
You have been arrested by the dictator of Whogivesafuckistan.
He hands you two boxes, 10 black balls and 10 white balls. He says you may place the black and white balls into the two boxes in any configuration you like.
The judge will, in one hour, pick a box at random and then pick a ball from within that box at random. If it is black, you will be executed, if it is white, you will be set free.
How do you place the black and white balls into the box in order to maximize the chance that you will survive?
>>344178589
Which means, in this hypothetical scenario, you'll always pick the gold ball first, because the deviser of the question has made it so.
Truly, we are like mad gods, creating such terrifying realities
>mfw any probability more than 50%
It's retarded. Here's an example:
A box has ten different colors of balls. You pick one randomly. What's the probability that the ball is red?
50%.
Either the ball is red or it's not. 50%
>>344178731
But you do, it says so in the question.
you pick a gold ball, it can only be from one of two boxes, this happened 100% determined, [g,g] would have one gold ball remaining, [g,s] would have silver, the answer is 50%, if you are saying 2/3 because the original chance you're ignoring the certain gold pick, if you think its 2/3 because g,g,s you forgot the first gold pick if the box is g,g , and if you think its 2/3 because of wikipedia fucking off yourself.
if you disagree I don't even care, this thread isn't even on topic.
>>344178735
doesn't say anywhere that you have to put the black balls in
>>344178735
Put one white in every box
Swallow all the black ones.
>>344178451
Again see this
>>344177785
You clearly don't understand the problem.
>>344178731
That is what is impliesd, yes. Pick a random box to get a guarenteed gold.
Just recreate this problem, restarting every time until you get a gold. It will always be fifty percent.
>>344168251
Huh...today I learned something useful on 4chan. Thanks anon!
>>344178848
>>344178957
It says you get a golden ball from a random box. You don't know which box it is.
>>344178206
That's assuming that the balls are all in one box. However you have two separate boxes. And you always get the gold ball first assuming. The case of one box doesn't affect the other box.
>>344178735
>If it is black, you will be executed
fucking racist baka
Let's label the balls. The gold balls in the Gold-Gold box are Ball A and Ball B. The gold ball in the Gold-Silver Ball is C.
>Situation 1: You pick up Ball A. Next ball you pick up will be Ball B.
>Situation 2: You pick up Ball B. Next ball you pick up will be Ball A.
>Situation 3: You pick up Ball C. Next ball you pick up will be silver.
Thus 2/3
>>344178735
Attack my captor with a volley of balls, escape prison.
>>344165727
Sauce on that pic
>>344178247
He's wrong.
>>344179028
Thatz the problem. It will either be 1 or 2. Random box... but guarenteed gold. Fifty percent.
>>344178702
Yeah, because you eliminated the crucial step that makes it 2/3, the fact that you already picked one ball at random and it turned out gold. You can't just eliminate that because the entire crux of the problem is the information you gain from knowing that. Retard.
leave it to /v/ to spend hours arguing about balls
>>344178514
You're picking boxes and then balls. And then the first ball you get just happens to be a gold.
>>344168768
airplane on treadmill
>>344179095
Situation 1 = situation 2.
This is case 1.
Situation 3 is case 2.
50%
Seeing 1 and 2 separate is the problem.
>>344179160
Or you're wrong.
Conditional probability is a THEORY. we could argue about it all day.
>>344178957
You can try exactly what you said and you'll get 2/3. 2/3 of the time you get a gold from your first selection, it'll be from the one with 2 golds; 1/3 of the time, it'll be from the one with 1 gold. It's as simple as that. The question is just tricking you into focusing on the 2nd box, when the 1st box is the one that matters.
>>344179196
Except there's two ways you can guarantee a gold from GG, and only one way you can guarantee a gold from GS.
It's more like:
G1G2
G2G1
G3S
These are the three situations where you can pick gold first, and only one of them ends in a silver.
>>344178206
Wrong. Considering what you said, lets break down all the ways you are wrong.
Lets consider each ball as a separate entity. What are the possibilities for the set?
1. Gold Gold.
2. Gold Gold
3. Gold Silver
4. Silver Gold
5. Silver Silver
6. Silver Silver.
That means that the set has two chances out of six. 2/6 is 1/3rd 33% chance for the set.
Now lets continue from where we got the Gold ball first.
You already have a Gold ball. The options are NOT
1.Gold Gold
2.Gold Gold
3.Gold Silver
They are IN FACT.
1.GOLD
2.SILVER
This is because your NEXT BALL IS ALL YOU CAN CONTINUE FROM. THE CHANCE THAT YOU PICKED A GOLD BALL FIRST IS NOT EFFECTED, THIS IS NOT THE CHANCE THAT YOU PICK A GOLD BALL FIRST AND SECOND, THIS IS THE CHANCE THAT THE SECOND BALL YOU PICK IS GOLD AND NOT SILVER.
This is a CLOSED SET. You cant bring meta knowledge into the closed set.
"Why not?"
Because if we bring in meta knowledge then why stop at assuming theres a greater chance of picking the gold ball? The entire set's probablity is 33% if we bring in the meta knowledge then the chance of getting the ball is 33% since the chance of getting two gold balls is 33%.
SO we only have the probability of the NEXT pick. There are two boxes where you CAN GET A GOLD BALL FIRST. And the Probability that you got the box with two gold balls is 50% out of the two boxes.
>>344168251
Makes sense, when you give it some thought. Still feel like a fool for thinking it was 50%. Still, isn't it a 50% chance, but a 2/3 probability?
>>344179303
If you had a 6 sided dice and 5 of the sides had A on it and the 6th side had B, you are arguing that since 1 = 2 = 3 = 4 = 5 there is a 50% chance you roll A or B. Do you not see how retarded that is?
>>344179309
>Conditional probability is a THEORY
Lol.
>>344178830
I love you, anon.
>>344171265
The number of balls in the all gold box is less important than the percentage.
100% gold for box 1.
50% gold for box 2.
You cannot ignore the original probability because it's extremely important.
If you drew 300 times, your distribution would look a lot like this
100 gold from box 1
50 gold from box 2
50 silver from box 2
100 silver from box 3
So in that distribution the gold from box 1 vs gold from box 2 distribution is not even.
Here's a better way to describe it.
Imagine that box 2 has 1 gold and 999 silver.
and box 1 still has 2 gold.
You randomly pick a box and draw a coin, it's gold.
What are the odds that it's from box 1 vs box 2.
>>344178957
>>344179364
Made a bit or a wording error here. For clarification:
The question is just tricking you into focusing on the 2nd selection, when the 1st selection is the one that matters.
>>344179505
We're talking about balls, not dice retard. Balls only have one side.
>>344179252
Again - your initial chance is indeed 50% of getting the two gold box. in a GG GS situation.
But the probability changes once you have some proceeding knowledge.
Now I see. The trick is the balls are absolute objects but "gold" is a classification of ball. Answer is 2/3.
>>344179620
actually they have infinite sides
>>344179407
You're full of shit. Are you a philosophy student or something?
If you don't believe the chance is 2/3 just try it yourself.
>>344179407
Not only do you not know how probability works, you don't know how causality works. That's like saying it doesn't matter who killed JFK because it happened in the past. We don't know where the gold ball came from, and that matters.
>>344179692
That's true. Thanks for correcting me.
It's double as likely to draw a gold ball from the box with two gold balls than from the box with only one.
This isn't really rocket science.
>>344178830
Best post ITT
>>344179407
You assume that the question is reduced to whichever boxes have golden balls, which is not the case. It's which golden balls are found in which boxes, since you pick balls and not boxes.
>>344179364
>2/3 of the time you get a gold ball from your first selection
No, ONE HUNDRED PERCENT of the time you get a gold ball because that's one of the questions initial conditions.
If I put two boxes in front of you, GG and GS, and I pluck out a gold and give it to you, and then say "draw again from the same box", the chance that the ball that is still in that box is 50%. It's either a gold or silver.
>>344179407
This anon gets it.
>>344178830
But you never said that one of the ten colors was red. They could very well be ten colors other than red! Or they could even be ten different shades of red!
>>344180132
Meant to say first box. Got the wording mixed up there and didn't notice
>>344180132
But there are 3 possible picks where the first ball is gold.
Of those, only 2 allow for the second gold to be picked.
It's 2/3rd.
>>344179523
>>344166613
>>344178451
Sorry to everyone in this thread that I called a retard. Upon further revision it would appear that I was wrong and that I am the retard.
It's 2/3's
It's 2/3 or 1/2 depending on your interpretation of the scenario.
I can't believe people are still arguing about this.
>>344179670
But it doesn't change the fact you have only two boxes with gold and the first gold is guaranteed.
>>344179690
>>344180253
Good, good.
>>344180132
>Flip a coin
>Coin lands on its side
>"Well gee, what are the odds of that!"
>"100% because it already happened lel"
- you
>>344180132
Except you drew that gold ball at random, meaning it probably came from the GG box. You should rephrase your statement to say:
"I pluck out a ball and look at it. If it's a silver I put it back without telling you and pluck out another one. If it's a gold I give it to you."
This is what's happening.
>>344180336
No, 1/2 is plain wrong.
>>344180336
It's 43%
>>344180397
It's guaranteed that the first ball is gold, but it's not guaranteed which of the three gold balls in the boxes it was. It's more likely to have come from the GG box.
>>344180336
>interpretation
What interpretation? There are three golden balls, two of them are in Box A and one is on Box B.
Now please tell me how likely it is that the gold ball came from box A.
>>344180693
>Now please tell me how likely it is that the gold ball came from box A.
That's not what the original question was.
>>344179690
No man
If you pick it from box one, there is a 100% chance the next ball will be gold.
If you pick it from box two, there is a 100% chance of it being silver
It is asking for the odds (more specifically) of picking up 2 golden balls, only taking into account the times in which a golden ball is pulled first. The first 2 options you provided are redundant.
>>344166710
Are you retarded?
>>344180468
>it probably came from the GG box
There's a 67% chance it came from the GG box. You call that "probably"?
You really are shit at statistics.
>>344179405
Lets recreate this problem 100 times in a row.
You get 50 50 golds and silvers from the 3 boxes. Lets eliminate the silver 50 leaving the gold 50s. This occures because the 33 guarenteed silvers instantly die while the half silvers are half chosen at random. 33 + 16/17.
Now you have 50(ish)gold from equal maths for getting gold. 33 guarenteed + 16/17 random. They all choose an additional ball, 25 25 gold and silver.
That, us, leaves about a 2/3 chance of the remainders being gold...
Well played I guess. It's 2/3.
2/3 assumes the balls are unique
1/2 blatantly answers the question posed
>>344180397
But the question is not - what box did you pick initially with no previous knowledge.
But the question is - what box did you pick now that you know one of the balls within it.
look at it inversely. - if you picked a silver as your first - you would know 100% that you picked a GS box.
As you you picked S1 from a G1G2 S1G3 set.
But if you picked a gold, it could be either G1, G2 or G3. You don't know which of the three you have picked. It's just more likely that you've picked from the set containing g1 and g2. Rather than from the set containing G3 and S1
>>344180810
No? Because the probability of the next ball being gold is logically the same as the gold ball in your hand being from box A. If the next ball is gold you had box A. If you had box A, the next ball is gold. They are functionally equivalent.
>>344180945
The balls are unique and always have been unique. Or rather, if there are two identical balls in a box you have a 50% chance of picking either one.
>>344180841
Thar third line was supposed to be different math. 33 + 16/17 silvers were dead while 33 golds were alive and 16/17 balls were unknown. Leaving 66 percent chance of gold. Just fixing that real quick.
>>344168401
This is the best way to explain it but I still can't decide if I think this way ro the 50% way
>>344180612
But it's not. If your first ball is guaranteed as a gold, that's just a given since both boxes have gold. You still have two boxes. This is not a mixed box. You either got the GS or the GG box. The GS box doesn't automatically get more golds just because the other box has double golds
just get some balls and boxes and test it out 1000 times
number of times you drew 2 golds divided by number of times you drew gold 1st is the probabilityit's 2/3
>>344181261
I can't even wrap my head around the way you misunderstand the situation.
>>344181261
It's not a given because you didn't pick 'the first' ball out of the box, you picked a random ball out of the box. It happened to be gold. It could have been any of the three golds in the two boxes.
>>344164016
Contradicting information. I ain't answering that bullshit.
>>344164016
I bet you followed a guide you fucking faggot.
>>344177137
Someone goofed this since the text does not describe the image
>>344181438
Right, and from there the second ball is either gold or silver. And there's a 1/2 chance it is gold.
>>344181584
reported for ontopic
>>344181018
The chances don't change the other boxes chances. You are mixing the boxes together. If the gold is guaranteed, then it's 50%.
Just proving the odds are 2/3 here
>>344181713
Was just about to post this
https://www.khanacademy.org/computer-programming/bertrands-box-paradox/6372168553725952
>>344181663
No. You have a gold ball in your hand, but you don't know if it's:
G1 (second ball will be G2)
G2 (second ball will be G1)
G3 (second ball will be S1)
>>344164816
It will always be lesser than One since you'll always be lacking an infinitesimal but tangential half of the last fraction added.
>483 replies
>>344181847
Sure, but it doesn't matter which gold ball you're getting. All that matters is that the ball is gold. Again, you're either getting a gold ball or a silver ball. There's only 2 options.
>implying I didn't put my 2 gold balls in your mother's box
>>344164016
I just upgraded to Windows 10 and tried running the Witness RIGHT BEFORE seeing this thread.
The shadows are all fucked up for some reason. So I'm probably downgrading again.
Almost done with the game. It's breddy darn gud.
I can't think of any games that make you feel quite as smart as that.
Maybe his first game. Braid. That's pretty great too, but not as pretty.
>>344177137
I think you meant this
And the odds are 2/27
imagine if you will that there are three gold balls and just one silver ball, of which two gold balls are in one set and the remaining balls in another set, and that there are no boxes, each ball is unique; you are to pick any gold ball, without knowing what set it belongs to, meaning that there are three possibilities
in two of the three possibilities, you have the set with the two golden balls, whereas there's only one possibility for the set with the gold and silver balls
it also makes it easier for some people if you tell them to number each ball in the original question
I think it comes down to this.
Label a gold, then it's 2/3 for that one.
Any gold, it's 1/2.
Don't know how to word this better, help?
>>344182012
>There's only 2 options.
And they have different probabilities. 2 options does not mean two equally likely options. If you take a gold ball out of a box you're more likely to have chosen the box with two golds rather than one, hence there's a greater probability the second will be gold.
>>344178517
Same outcome doesn't mean same probability mofo.
It's two thirds, or 66.66.., not fity fifty.
>>344181796
>>344181713
Fug, should've posted that at the beginning of the thread. Then there wouldn't have been a need for hundreds of replies arguing over balls.
>>344182012
It does matter, because if it's G1 or G2 the second ball will be gold, and if it's G3 the second ball will be silver.
>>344182325
People would have still argued.
>>344182325
>implying it would change anything
>>344180841
>>344181202
Reposting the math. The first round of eliminations was 50 silvers. Because of the guarenteex 33 and the random 33 splitting gold and silver to 17 silvers at first pull. Second round of eliminations would result In 33 guarenteed golds and 17 random golds as well as 17 random silvers. The second round of eliminations (op`s problem) is without a doubt 66% gold to 34% silver. Give or take 1%. Am I wrong?
>>344181713
>php
absolutely haram
>>344182012
Yes, and those two options do not have equal probabilities. What is it with retards in probability puzzles always thinking that two outcomes must always have a 50% chance of occurring? That same thing is why people have so much trouble with the Monty Hall problem.
>>344164016
Its Conditional Probability problem just like the goat problem.
If you fucks dont know how to calculate with conditional probabilities and the bayes formula then dont shit up the thread like these retards that say 50/50 for the monty hall problem.
>>344181796
I'll never understand why some JS coders have such a hard on for anonymous functions/function assignment and fake classes for simple single use codes.
I'm working on a project at the moment which is full on unreadable spaghetti code due to constant callbacks and hard to parse function assignment.
"but if we organise it like this is makes it easy to reus"
NO YOU HAVEN'T REUSED A SINGLE PIECE OF CODE YOU SHIT, THIS SITE IS FULL OF 50 DIFFERENT AJAX FORM LOAD/SUBMISSIONS, I'VE YET TO SEE YOU DO ANY POLYMORPHISM IN THIS PROJECT
Sorry to rant but I'm working on a site at the moment that's about a year over-due.
>/v/ talking about balls
Why am I not surprised?
Fucking faggots all of you
>>344182256
>>344182368
>>344182427
Yes, the odds are equal. You have 2 options. You either pull out a silver ball or a gold ball. It's black and white, and there is a 50% chance you'll get the gold you're looking for. Slapping on a bunch of other irrelevant information does not change this fact.
>>344167369
All of you 2/3 retards didn't read the fucking question.
You picked ONE box that had a gold one in it. This eliminates the silver box and leaves us with two possibilities:
>The other is gold
>The other is silver
What are the odds that the first one is true? Given the two probabilities, the answer is 1/2
>>344182551
The goat problem is conditional, but doesn't need any amount of extra calculation because of it, though.
That one just needs a bit of extra understanding.
This really isn't in the same category, as the box with two silver is specifically left out in the setup.
>>344182684
>you either win the lottery or you don't :^)
>>344182679
I'll suck your dick you faggot
>>344182684
Watch out, anon, next time you go outside you could be fine or you could die horribly in an accident. That's two options, so it's 50-50.
>>344182794
It's not 'the box you picked has a gold in it.' It's 'you picked a gold at random. Which box is it more likely to be, based on this?'
So the answer is 2/3, but I just can't understand why.
If I pulled out a gold ball, the odds of the remaining ball in there being gold is 50%, because it either contains 1 gold ball or 1 silver ball. Fucking probability.
>>344182794
If you picked a gold you are twice as likely to have picked box 1 over box 2. LOL.
>>344182924
>you could be fine or you could die horribly in an accident. That's two options, so it's 50-50
technically...
>>344182830
Yeah, the double silver really never comes into play, does it?
>>344182964
You are twice as likely of having picked the first box because it has 2 golds. That's the thing most people don't understand.
>>344182408
Of the 50 golds left behind, we would get 17 + 17 golds and 17 silvers. 2/3. this would only add up to 34 golds. but 17 of the random silvers would get their second round as 17 + 17 silvers and 17 golds.
Within the confines of drawing first gold, the answer is without a doubt 2/3.
>>344183008
No it isn't even technically true.
>>344182978
This.
Odds are still in the player's favor because of the available information.
>>344183196
I suppose you could get maimed but still be alive.
So 33% then?
>>344183008
>technically...
No.
>>344183303
Could be Superman
0%
>>344182684
Woah, equal odds of winning the grand lottery prize or NOT winning the grand lottery prize?!
I need to play more often!
>>344183410
Fuck you. I have kryptonite so it's 100%
>>344182837
Yes? I'm not really sure what you're getting at. If the lottery numbers were set up the same way as the balls in OP's question, then yeah, it's still 50% chance. Three entrants, one is disqualified because the first number is not on his ticket. The other two have the first number, now there's a 1/2 chance the next number will be theirs (because the second number can only be 1 or 2).
>>344182924
Great argument, anon.
>>344183415
Yes.
>>344183167
But if you always pull a gold on your first draw, it doesn't matter what box you picked because the probability is 100%?? That part is irrelevant to the question, because we're talking about the probability of the second draw.
>>344183415
> he hasn't won the lottery at least 5 times in his lifetime
Get a load of this fucking pleb everyone
It's 1/2 fuckers. 3 Gold balls, 3 Silver balls. 50%
>>344183490
Immunity cat.
>>344183538
The probability of picking a gold ball is 100%, the probability of picking a gold ball from box A is 66%, the probability of picking a gold ball from box B is 33%.
>>344183628
It's 50% but not for that reason, box 3 doesn't count.
>>344183193
>>344182408
>>344181202
>>344180841
Can someone please check my math?
>>344181921
if its infinitely close to the number, it is that number
>>344164016
Play Catherine, it's an amazing sense of achievement finally beating the higher levels and Axis Mundi
>>344183628
>using retard logic but still getting the correct result
>>344183786
If it doesn't count why is it there?
>>344178830
/thread
>>344183943
To trick you. Just like much of the other information given.
>>344183943
Smoke and mirrors
Don't let them take you.
>>344183528
No, that's not how it works. Lottery numbers are revealed in order. The balls are drawn at random. If they say the winning ticket has a 1 on it, you could win with 11, 12, or 21. And then the following condition is that the 1 has to be in final position. And that's it. That's the lottery. Of the three preliminary candidates, two have won.
>>344183528
Does looking stupid on purpose give you some kind of kick?
>>344168878
Trouble with the trolley dilemma, eh?
>>344183773
You mean the chance of the gold ball being picked from A is 66%, right? I think I'm starting to get it.
I almost failed my statistics exam last year so I'm not surprised that I'm finding this difficult lel
>>344184238
Yup. You have a gold ball, no doubt about that. But there are three gold balls it could be, and two of them come from Box A.
>>344184238
That goes for the first ball. The second one is an entire different scenario.
>>344183786
Then why is it 50% then?
Because I'm pretty sure it's not. And it's pretty easy to empirically prove whether it's the case.
>>344184354
No. If the gold ball in your hand is from Box A, then there's a 100% chance the second ball is also gold.
>>344184354
You can't just toss out the first scenario. There might as well just be a box with a gold ball and a box with a silver ball in that case.
50% Win or lose, there is no tie.
>>344182794
>You picked ONE box that had a gold one in it.
Ah, this is the part where you stumble.
In fact, you would be completely right if the problem were this instead of the one in the OP:
>You pick a box at random.
>The box you picked had at least one gold ball in it.
>What is the chance that the picked box has two gold balls in it?
In that case it would be 50/50. Two boxes have at least one gold ball in them, and no matter which of those boxes you picked it would be an equally true statement. But that's not what happened. You didn't just "Pick a box with gold in it", you picked a RANDOM ball from a box, and that ball happened to be gold. This tells you more about the box than "it had at least one gold in it", because the gold was the one you randomly picked. If it was a G/S box, then there was only a 50% chance to have picked the gold in it. If it was the G/G box, then there was a 100% chance that you would have picked a gold ball from it. You definitely picked a gold ball, so you can conclude that it is more likely that you picked the box that only has gold balls.
>>344183528
The indistinguishability of the ball (in this scenario the 'order' of the lottery pick) is important. If the balls were labelled: [G1, G2] [G1, S1] and you were told the ball you got what G1 it would be different.
>>344184353
So I understand that, but I don't understand why that matters. This question is entirely concerned with the second draw, and the probability that the remaining ball is gold or silver is 50/50 because you removed a gold ball from the GS or GG box.
I'm ready to give up on this when you are, just say when and call me a retard.
>>344182964
It's because the second action isn't a choice per see.
Put it this way - you know you have 3 gold balls and you know you have picked up one. You have no idea which of those 3 you have picked. But it's more likely that you picked up one from the box with two, rather than the one from a box of one.
>>344184141
Again you are tacking on more information that you have pulled from your ass. There are three results possible in my theoretical lottery: 1-1, 1-2, and 2-2. Yes, I know, it's not like a real life lottery. Nor is pulling 2 balls from a box.
The first number read off is 1. The 2-2 person is eliminated because they cannot win. Then the next number is either going to be a 1 or a 2. There's a 50% chance for both. At this point, yes, you either win or lose. Which is what the original question in the OP is asking. The information that came before is irrelevant.
>>344184184
Fuck off, retard.
>>344184443
>>344184472
If I have A I pick gold, if I have B I pick gold. This is one scenario because it's the same box, even though there's two balls this doesn't matter.
If I have C I pick silver.
The next one yiu pick is either gold, gold or silver, that is true. However read it as this :
The next one you pick is (gold A or gold B) or silver. 50%.
>>344184709
Think of it this way. You've pulled out a gold ball. This leaves the following situations:
It's gold ball 1, in which case the next one will be gold ball 2.
It's gold ball 2, in which case the next one will be gold ball 1.
It's gold ball 3, in which case the next one will be silver ball 1.
These three situations are equally likely, but two of them end in a gold ball being drawn second. The second draw is dependent on the first.
