Bayes Theorem

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komark

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Jun 12, 2010
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Here is the problem. You have 5 coins in your pocket. 2 double headed, 2 fair, and 2 double tailed. You pull one out and it lands heads up. What is the probability that the bottom of the coin is heads? I am pretty sure you use Bayes Theorem for this problem, but I am not sure what goes where. I made this chart:

H T Total
HH 2 0 2
HT 0 2 2
TT 0 1 1
Total 2 3 5

I know the formula asP(A/B) = [P(A)*P(B/A)]/P(B)

I think P(A) = 4/5 and P(B/A) = 1/2 but am not sure of what P(B) is even asking for. After performing simualations the result should be 2/3?
 
There are 5 coins?. But there are 6 listed: 2 fair, 2 double heads, and 2 double tails.
 
What is the probability it is the double headed coin given the first flip is heads?.

\(\displaystyle P(DH|H)=\frac{P(DH)P(H|DH)}{P(H)}\)
 
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