If the probability of event A PA077 the probability of event

If the probability of event A, P(A)=0.77, the probability of event B, P(B)=0.64 and the probability of B given A, P(B|A)=0.73, find the probability of A given B, P(A|B).

Solution

P(A)=0.77   P(B)=0.64   P(B|A)=0.73

now P(B|A)=P(AB)/P(A)

so P(AB)=P(B|A)*P(A)=0.73*0.77=0.5621

now P(A|B)=P(AB)/P(B)=0.5621/0.64=0.87828 [answer]