Let A and B be two events in a sample space S such that PA

Let A and B be two events in a sample space S such that P(A) = 0.5, P(B) = 0.5, and P(A ? B) = 0.3. Find the probabilities below.

(a)    P(A|B)

(b)    P(B|A)

Solution

(a)    P(A|B) = P(A and B)/P(B) = 0.3/0.5 =0.6

(b)    P(B|A) = P(A and B)/P(A) = 0.3/0.5 =0.6