You flip two coins.
At least one of them is heads.
What are the odds that they are both heads?
>>46707531
50%
>>46707531
33.3% repeating, of course
>>46707531
Yes
it's 1/3
Look at all the possibilities:
HH
TT
HT
TH
All we do is ignore the ones without any heads, that is TT, and we're left with three options. only of of those three has both heads.
>>46707717
There's already one confirmed as heads you stupid idiot, it's 50/50 because there's only HH and HT
>>46707572
This would be true if the question was phrased: "You flip two coins, if first coin was heads, what are the chances second coin was heads as well?"
>>46707531
Now riddle me this: "If I flip a coin, what are my chances of getting a head?"
>>46707740
please do not call people names. especially when you're wrong.
>>46707531
chance of the first one landing on heads:
>0.5
chance of the second one also landing on heads:
> 0.5×0.5=0.25
> 25%
What the fuck /tg/?! I though you guys were smart when it comes to stochastics.
>>46707775
I don't see any reason not to call people names on a website where we have no names.
>>46707797
See if we're concerned about both being heads and one is already confirmed to be heads, it's not a 25% shot. It's a 50/50 shot.
>>46707797
wrong. this assumes that it's possible for both coins to not land heads.
>>46707797
Someone clearly doesn't know how to bayes.
P(HH| d = {}) =25%
P(HH| d = {H}) is a different problem.
So let's consider our options for the first problem,
P(HH| d = {})
TT
TH
HT
HH
Given at least one of the coins is already heads we now have
P(HH| d = {H})
TH
HT
HH
As a result there exists a 1/3 chance that both coins are heads.
>>46707740
This is true ASSUMING that the FIRST coin is heads. OP said that "a" coin is heads, it could be the second one.
Source:
I'm an engineer
>>46707846
It doesn't matter which coin is heads because we're trying to figure out the odds of getting HH as long as one coin is H.
>>46707917
You are looking at this the wrong way.
Two coins are flipped. Usually, there would be four possible outcomes:
TT
HT
TH
HH
However, we are told that one of them is going to be Heads regardless, which removes one of the possible outcomes. So now it's
TH
HT
HH
And Which gives you 2/3 for one Heads, one Tails and 1/3 for double Heads.
The coinflips here are not a sequence. You don't flip one coin that is always going to be heads and then flip another one (which would make it 50%)
You flip both at the same time, but there are only three possible outcomes.
It's not intuitive, though.
>>46707967
Yea, you if you're flipping both at the same time it's not going to matter if it's TH or HT because either way there's one heads.
>>46708000
It matters, because it's still two distinct cases.
You don't have a 25% chance to flip TH, a 25% chance to flip HT and a 50% to flip HH.
>>46707531
In this precise wording, it's 50/50, but didn't you have enough trolling on /pol/ with the montehall problem?
>(H)T
>T(H)
>(H)H
>H(H)
>Flip one coin. Lands on heads.
>Wait one minute
>What are my odds of getting HH when the first coin flipped is already an H.
>Some anon goes %33
It's 1/3rd.
>>46707917
It absolutely does.
>>46708057
That isnt the problem that we're solving here
>>46708057
>Flip one coin. Lands on heads.
Nope. It could have landed tails. In which case, the other coin would have to be heads.
It's fascinating to me how difficult this is for some people.
>>46708050
>(H)H
>H(H)
lmao
>>46708174To be honest I'm mostly just enabling OP.
>>46708189
>You flip two coins.
>At least one of them is heads.
>What are the odds that they are both heads?
So we have one of two results.
>(?)H
>H(?)
Now here are all possible results.
>TH
>HH
>HT
>HH
Two of the four possible results are HH, so the odds are 50:50. Explain to me why you believe this is incorrect.
>>46708189
It's basically a rewording of the Monty Hall problem. It seems so "intuitive" that it's 50/50 that people who are otherwise pretty rational don't can't see it any other way, even when the math is in front of them.
http://marilynvossavant.com/game-show-problem/
http://priceonomics.com/the-time-everyone-corrected-the-worlds-smartest/
>>46708337
It is in fact not a Monty Hall problem
>>46708337
This is not a Monty haul problem. The Monty hall problem involves 3 outcomes in which 1 outcome has already been determined. This is a problem in which there were initially 4 different outcomes and now there are only two outcomes.
>>46708398
>there were initially 4 different outcomes
Wrong.
>>46708398
There were never 4 outcomes. There were 3. TT is not a possible combination. See >>46708174
>>46708465
What were the three possible outcomes? Also let me get my little dice rolling app and see how often you get a 2 on a d2.
>mfw people still fall for this bait
Think of it like this.
You flip two coins. Before you see the result, someone puts his hands over the coins, then says "I guarantee it's not HH".
There are three possible results now, TH, HT and TT.
It's 33%.
People say "it's 50%" assume that you flip one of the coins first, which comes as T, and then they flip the other one. But the question does not state such a thing at all.
>>46707531
>At least one of them is heads.
>>46708744
The TT result can happen twice.
>(T) H
>(T)T
>H(T)
>T(T)
So 2/4 outcomes are TT, so 50%
>>46707531
I remember you, dipshit. I'll give you the same answer /sci/ did last time you made this thread: Undefined, because the question is incomplete.
>>46708832
>The TT result can happen twice.
No it can't.
>>46708832
>Coin 1 can be tails and Coin 2 can be tails, but also Coin 1 can be tails and Coin 2 can be tails
This is what you just said.
>>46708893
do you actually think there is just one person on 4chan who makes math threads?
are you retarded or are you just new here?
If the intent was to say "one roll is confirmed already to he heads", then the chance is 50%. In game terms, this would be something like "you have a 50% crit rate on your attacks, but thanks to another effect your next attack auto-crits."
If not, the chance is 33.33_% as explained already.
>>46708935
As far as I'm concerned all people who do the same thing are the same person. From my perspective there's no way to tell either case for certain, but they produce the same post regardless. Why bother differentiating identical idiots?
>>46708965
>If the intent was to say "one roll is confirmed already to he heads", then the chance is 50%
Wording it that way doesn't get you away from 1/3rd chance either. You didn't specify which roll was heads.
The only way you could possibly get 50% is if the question was "Coin 1 is heads. What are the odds that Coin 2 is also heads?" That is neither the question in the OP nor the question you just asked.
>>46709015
No, if both coin flips are hidden, and then one is revealed to be heads, the chance of the other being heads is 50%, doesn't matter which was first.
>>46708893
I don't post on /sci/, dipshit. But it sounds like this is now the 2nd time you've gotten this question wrong.
>>46709094
This is not the first time this problem has been posted.
Last time it was posted with crit instead of heads and die rolls instead of coin flips, and it was originally posted on /int/ who argued about it for hours, reported it here in the hopes that we'd do better, and when we had the same argument took it to /sci/, who argued briefly until someone called out the ambiguity of the question.
>>46707835
Notice how none of the 50%tards are responding to this post.
>>46707835
But it was the first flip that got H, so there's no chance to get TH.
It's HH or HT, that's it.
>>46709414
>it was the first flip that got H
you can't read.
>>46709414
Nowhere does it say that "the first flip is H." You literally just made that up.
>>46709488
It's either the first flip or the second flip. I can see where you are coming from, but I'm talking about after the first die is rolled.
>>46707531
1 chance out of 3 possibilities. So 33.3~%
>>46709605
>It's either the first flip or the second flip
>it was the first flip that got H
Pick one.
>>46709732
correct
>>46709732
Aaaand thread over.
Wow, you guys will argue over anything...
>>46713934
That's clearly a bouncy castle.
>>46714010
It's a bounce house
BOUNCE
HOUSE
>>46714082
What kind of house has bastions? It's a castle.
>>46707531
It's one in three, but only because you require at least one to be heads.
>>46707531
What is the probability of getting this answer correct?
a) 25%
b) 50%
c) 25%
d) 75%
If I flip a coin, what's the chance of me getting head off your wife?
>>46715740
0, she doesn't blow gays
>>46715698
but that's not even a trick question or a paradox, the answers just none of them so zero%.
It can't be 25% because a and c are the same.
It can't be 50% because there are not two answers with 50 %.
it cant be 75% because there are not 3 options with 75%
thats no more a complicated question then
"what is the probability of flipping 2 coins and getting heads twice?
a) 100%
b)150%
c) denmark
d) potasium
>>46716201
What's the probability that this anon I'm replying to is autistic?
a) 100%
b) 1
c) 100/100
d) 2(.5)
>>46707531
Well: If, other than heads, there's unlimited options about the coins appearence, I'd say the odds are fairly small.
>>46707531
I would say that 50% anons are trolling except I've tried to explain this problem to computer engineering students who TOOK A PROBABILITY COURSE IN UNIVERSITY and they still haven't grasped the math behind it.
>>46717879
if im being honest, i thought it was 50% too until i saw >>46709732
>>46707531
https://en.wikipedia.org/wiki/Boy_or_Girl_paradox
Cannot determine the answer until you specify how the scenario is set up. If you flipped one coin for heads and then are asking about the second coin, then 50%. If you took a sample from a random population, displayed one head from each sample, then ask if the second is heads as well, then 33%.
>>46716140
She married you, didn't she?
>>46719789
Typically when this kind of question is posed, the scenario is as such: your friend flipped two coins without letting you look, looks at them, then tells you at least one is heads, and now you have to state the probability of them both being heads.
Presumably if they got TT they would re-flip the coins, or rephrase the question and tell you at least one is tails.
Which means, of course, when the question is asking the odds of two heads when one is guaranteed, the chances are 33%, and when the question is asking the odds of two tails when one is guaranteed, the chances are 100%.
>>46707582
Well, that's a lot better than we usually have.....
>>46719789
>If you flipped one coin for heads and then are asking about the second coin, then 50%.
If you could read, you would know that this is not the question that was asked.
>>46719838
Come up with a joke that makes sense, and try again.
>>46714010
>>46714082
>>46714164
It's a moonbounce, morons.
>>46709062
Still not the question asked.
>>46707835
Awesome Bayesian breakdown.
>>46720507
All right chums, time's up, let's do this...
>>46727148
Wasn't that him asking if buffs were up?
>>46727153
I don't remember, there's like a full minute between with a lot planning before Schulz comes back and rushes in screaming leeroy jenkins or something
>>46709732
Sorry if I'm being silly, but doesn't that assume that the 3 possibilities have equal weighting, though? I mean...
>>46707531
>>46709175 seems to have a point, I feel like the question is a little ambiguous, given that it's not stated how the "at least one heads" statement is enforced.
Is the whole question reset if TT occurs? Is one coin elected at random to have the heads state forced upon it?
>>46729045
The possibilities do have equal weighting, assuming that we're dealing with a fair coin (i.e., 1/2 chance to toss heads, 1/2 chance to toss tails), and that both events are independent of each other (the chance for throwing tails/heads on a particular toss are the same for the second toss, no matter what you tossed firstly).
Each combination occurs 1/4 times (TT, HT, TH, HH). These are the chances for arriving at one of the particular combinations when you toss two coins.
>I feel like the question is a little ambiguous, given that it's not stated how the "at least one heads" statement is enforced.
I don't really, although I admit I read it wrong the first time as well. "At least one of them is heads" clearly implies that it could be the first one, the second one, or both. One of these events occurs 3/4 times (HT or TH or HH).
>Is the whole question reset if TT occurs?
No, you simply dismiss those results, since you're only interest lies with those three possible events where you have at least one times head.
>Is one coin elected at random to have the heads state forced upon it?
You should read the question like this:
If you toss a set of coins an infinite number of times, take each instance where it came up heads at least once (which would be 3/4 times).
Of those instances, how many times did you toss HH. This simply is the chance of throwing HH divided by the chances of the events of interest.
Summarized: Of those 3/4 times where you throw heads at least once, how many times did you throw HH? That's (1/4)/(3/4)= 4/12 = 1/3.
Sorry for bad english.
>>46729045
>doesn't that assume that the 3 possibilities have equal weighting, though?
Yes. That is how coin flips work.
