The prior probabilities for events A and A, are P(A1) = 0.40 and P(A2) = 0.60. It is also known that P(A, N AZ) = 0. Suppose P(BA) = 0.20 and P(B|A2) = 0.05. a. Are events A and A, mutually exclusive? Yes Explain. (1) P(A: 0 A) = 0 (ii) P(A1) + P(A2) - 1 (iii) P(A2) + P (Az | A) (iv) PA2) - P(A2I A) choice ) V b. Compute P(A, B) (to 2 decimals), Compute P(A2 A B) (to 2 decimals). E. Compute P(B) (to 2 decimals), d. Apply Bayes theorem to compute P(A1B) (to 4 decimals). Also apply Bayes theorem to compute P(A,B) (to 4 decimals). de l'edback Partially Correct