Thread: Conditional Probability brainteaser

Suppose I flip two coins without letting you see the outcome, and I tell you that at least one of the coins came up heads. What is the probability that the other coin is also heads?

Through cond prob. I think the answer is 1/4, but others are saying its 1/3. There are 4 possible combinations, and knowing that at least one coin turned up heads doesnt change the probability of getting HH in flipping 2 coins.

we cant just eliminate TT from the equation bc before you flipped the coins, TT has 1/4 chance of turning up.

But if you said right from the start that the coins are somehow biased that at least 1 coin will always turned up heads, then i would agree that the probability of getting HH is 1/3.

otherwise if getting HH, HT, TH or TT have equal chances, then it should be 1/4.


Thoughts?

For me the answer is 1/3

HH HT TH TT have equal chance in general.

One of the coins is head, this means that only

HH HT TH

are possible, all with equal chance.

-> 1/3

Originally Posted by wnvl

For me the answer is 1/3

HH HT TH TT have equal chance in general.

One of the coins is head, this means that only

HH HT TH

are possible, all with equal chance.

-> 1/3

I still think that you can't eliminate the proability of TT in calculations just because one is heads after the fact.

Yes you can, because the chance for TT is zero after telling that at least one of the coins came up H.

Another way of looking at this problem: I have a bag with 1 red, 1 blue, 1 green and 1 black marble. I pull a marble out. At this point the probability are:





Which makes sense. I have 100% chance of having 1 marble if I pull 1 marble.

Now I look at it and tell you its NOT black. The chances are now





Again i have 100% of having at least 1 marble in my hand.

If I tried to insist the probabilites remained .25 for the colors I'd have this:





Which is saying after pulling 1 marble out of the bag, looking at it and saying its not black. There is now a 75% chance of me having a marble in my hand. Which is obviously absurd I definitely have a marble in my hand.


Now you can equate this:
red = HH
green = HT
blue = TH
black = TT.

Now telling you that at least one coin is Heads is the same as saying its not black. So the odds of double heads coming up (red) is 1/3.