4.72 Bayes' Rule A sample is selected from one of two populations, S and S2, with probabilities P(S) = 0.7 and P(S2)=0.3. If the sample has been selected from S, the probability of observing an event A is P(AS) 0.2. Similarly, if the sample has been selected from S2, the probability of observing A is P(A|S2)=0.3.

a. If a sample is randomly selected from one of the two populations, what is the probability that event A occurs?

b. If the sample is randomly selected and event A is observed, what is the probability that the sample was selected from population S? From population S?