Probability that Bill told the truth problem

[loganblacke]

Bill tells the truth one-half of the time and Harry tells the truth two-thirds of the time. Bill says something, and Harry, who knows whether Bill told the truth, says, "Bill just told the truth". What is the probability that Bill told the truth?

Let:
B = Bill told the truth
B' = Bill lied
H = Harry told the truth
H' = Harry Lied

P(B) = .5
P(B') = .5
P(H) = 2/3
P(H') = 1/3


So there should be 4 possible outcomes.. (H|B), (H'|B), (H|B'), (H'|B').

I know that there is an equation for each of these, like P(H|B) = P(H|B)/P(B|H) or something like that I'm just not sure which equation to use. Please help! Thanks!

 

[spamiam]

http://en.wikipedia.org/wiki/Conditional_probability" may help.