The prior probabilities for events A, A2, and A3 are P(A) = 0.30, P(A2) = 0.50, and P(A3) = 0.20. The conditional probabilities of event B given A1, A2, and A3 are P(B | A) = 0.40, P(B | A2) = 0.30, and P(B | A3) = 0.50. (Assume that A1, A2, and A3 are mutually exclusive events whose union is the entire sample space.) (a) Compute P(B n A), P(B n A2), and P(Bn A3). P(BA) = P(BA) = P(BA3)= (b) Apply Bayes' theorem, P(A, B) P(A)P(BIA) to compute the posterior P(A)P(BA) + P(A2)P(B | A) + + P(A)P(B | An)' probability P(A|B). (Round your answer to two decimal places.) (c) Use the tabular approach to applying Bayes' theorem to compute P(A | B), P(A | B), and P(A3 | B). (Round your answers to two decimal places.) Events P(A) P(B | A,) P(A, B) P(A|B) A1 0.30 0.40 A 0.50 0.30 A3 0.20 0.50 1.00 1.00