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.
>>344164816
Okay
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%
>>344169165
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.
>>344164016
>>344169332
>>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].png")
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.
