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Events A_1, A_2 and A_3 form a partiton of the sample space S with probabilities P(A_1) = 0.1, P(A_2) = 0.1, P(A_3)= 0.8. If E is an event in S with P(E|A_1) = 0.3, P(E|A_2) = 0.5, P(E|A_3) = 0.4, compute P(E) = P(A_1|E) = P(A_2|E) =
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