Yes, this is question 3 on page 103 of statistics and probability with applicati

Question

Yes, this is question 3 on page 103 of statistics and probability with applications for engineers and scientist by Gupta and Guttman. Suppose that A1, A2, A3,                    A4, and A5 are five mutually exclusive and exhaustive events in a sample space S, and Supose that P(A1) = 0.2, P(A2) = 0.1, P(A3) = 0.15, P(A4) = 0.3, and                    P(A5) = 0.25. another event E in S is such that P(E/A1) = 0.2, P(E/A2) = 0.1, P(E/A3) = 0.35, P(E/A4) = 0.3, and P(E/A5) = 0.25. Find the probabilities                    P(A1/E), P(A2/E), P(A3/E), P(A4/E), and P(A5/E).

Explanation / Answer

P(X/Y)=P(X INTERJUCTION Y)/P(Y)

P(E INTERJUCTION A1)=0.2*0.1=0.02

P(E INTERJUCTION A2)=0.1*0.1=0.01

P(E INTERJUCTION A3)=0.15*0.35=0.0525

P(E INTERJUCTION A4)=0.3*0.3=0.09

P(E INTERJUCTION A5)=0.25*0.2=0.0625

P(E)=ADDITION ALL ABOVE VALUES=0.235

P(A1/E)=0.02/0.235=0.085

P(A2/E)=0.01/0.235=0.04255

P(A3/E)=0.223

P(A4/E)=0.383

P(A5/E)=0.2659

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