@Mathematics There are 2 things that make me happy, girls and money. P(G) is the probability that a girl goes out with me, and P(M) is the probability I receive money.

P(G) = 0.3
P(M) = 0.1

P(H|G and M) = 1
P(H| not G and M) = 0.9
P(H| G and not M) = 0.9
P(H|not G and not M) = 0.1

find P(H), the probability that I am happy. @Mathematics

Question

@Mathematics There are 2 things that make me happy, girls and money. P(G) is the probability that a girl goes out with me, and P(M) is the probability I receive money.

P(G) = 0.3
P(M) = 0.1

P(H|G and M) = 1
P(H| not G and M) = 0.9
P(H| G and not M) = 0.9
P(H|not G and not M) = 0.1

find P(H), the probability that I am happy.   @Mathematics

anonymous · Answer

0.399?

anonymous · Answer

how did you work out that answer?

anonymous · Answer

Is it right?

I use P(A|B) = P(A^B)/P(B).  And P(A) + P(~A) = 1.  Also P(A) = P(A^B)+P(A^~B).  Specifically, G^M v G^~M v ~G^M v ~G^~M = U (the whole universe).|dw:1319483729988:dw|So H can be found by summing up its intersections with each of these events.  Let me know if you need more explanation.