The prior probabilities for events A1, A2, and A3 are P(A1) .20, P(A2) .50, and P(A3)

.30. The conditional probabilities of event B given A1, A2, and A3 are P(B  A1) .50, P(B  A2) .40, and P(B  A3) .30.

a. Compute P(B A1), P(B A2), and P(B A3).

b. Apply Bayes’theorem, equation (4.19), to compute the posterior probability P(A2  B).

c. Use the tabular approach to applying Bayes’ theorem to compute P(A1  B), P(A2  B), and P(A3  B).

Applications