3 The prior probabilities for events A 1 , A 2 , and A 3 are P(A 1 ) 30, P(A 2 ) 50, and P(A 3 ) 20 The conditional probabilities of event B given A 1 , A 2 , and A 3 , are P(B A 1 ) 30, P(B A 2 ) 40, and P(B A 3 ) 50 a Compute P(BA 1 ), P(BA 2 ), and P(BA 3 ) b Apply Bayes' theorem, equation (4 19), to compute the posterior probability P(A 3 B) c Use the tabular approach to applying Bayes' theorem to compute P(A 1 B), P(A 2 B), and P(A 3 B)

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Question: 3. The prior probabilities for events A 1 , A 2 , and A 3 are P(A 1 ) = .30, P(A 2 ) =

3. The prior probabilities for events A₁, A₂, and A₃ are P(A₁) = .30, P(A₂) = .50, and P(A₃) = .20. The conditional probabilities of event B given A₁, A₂, and A₃, are P(B|A₁) = .30, P(B|A₂) = .40, and P(B|A₃) = .50.

a. Compute P(BA₁), P(BA₂), and P(BA₃).

b. Apply Bayes' theorem, equation (4.19), to compute the posterior probability P(A₃|B).

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

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