10 Computing Probabilities The prior probabilities for events A1 and A2 are P(A1) 5 0 40 and P(A2 ) 5 0 60 It is also known that P(A1 A2 )5 0 Suppose P(B A1) 5 0 20 and P(B A2 ) 5 0 05 a Are A1 and A2 mutually exclusive Explain b Compute P(A1 B) and P(A2 B) c Compute P(B) d Apply Bayes theorem to compute P(A1 B) and P(A2 B)

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Question: 10. Computing Probabilities. The prior probabilities for events A1 and A2 are P(A1) 5 0.40 and P(A2 ) 5 0.60. It is also known that

10. Computing Probabilities. The prior probabilities for events A1 and A2 are P(A1) 5 0.40 and P(A2 ) 5 0.60. It is also known that P(A1ù A2 )5 0. Suppose P(B | A1) 5 0.20 and P(B | A2 ) 5 0.05.

a. Are A1 and A2 mutually exclusive? Explain.

b. Compute P(A1ù B) and P(A2 ù B).

c. Compute P(B).

d. Apply Bayes’ theorem to compute P(A1 | B) and P(A2 | B).

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