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, ) = 0.20 and P(B | A, ) = 0.05. (a) Are A, and A, mutually exclusive? They -Select-v mutually exclusive. How could you tell whether or not they are mutually exclusive? O P( A, ) = P(A, I A, ) O P ( A, n A , ) = 0 O P ( A, ) + P (A, ) = 1 OP(A, ) = P(A, 1 A2 ) O P(B | A, ) = P(B | A2) X (b) Compute P(A, n) B) and-P(A, n B). P(A, ( B) - 0.09 X P(A, ( B) - 0.05 X (c) Compute P(B). 0.115 X (d) Apply Bayes' theorem to compute P(A. ] B) and P(A, | B). (Round your answers to four decimal places.) P(A, | B) = 0.783 X P(A, | B) = 0217 X