The prior probabilities for events A, and A, are P(A, ) = 0.40 and P(A,) = 0.60. It is also known that P(A, n A, ) = 0. Suppose P(B | A. ) = 0.15 and P(B | A, ) = 0.05. (a) Are A, and A, mutually exclusive? They are mutually exclusive. How could you tell whether or not they are mutually exclusive? O P(A, ) = P(A, 1 A 2 ) O P ( A , ) # P( A , | A 1 ) O P(B | A, ) = P(B | A2) O P (A, ) + P(A2 ) = 1 O P ( A , n A , ) = 0 (b) Compute P(A, n B) and P(A, n B). P(A, n B) = P ( A, n B ) = (c) Compute P(B). (d) Apply Bayes' theorem to compute P(A, | B) and P(A, | B). ( Round your answers to four decimal places.) P(A, | B) = P(A, | B) =