Question: Problem 4-23 (Algorithmic) Suppose that you are given a decision situation with three possible states of nature: S 1 , S 2 , and S

Problem 4-23 (Algorithmic)

Suppose that you are given a decision situation with three possible states of nature: S1, S2, and S3. The prior probabilities are P(S1) = 0.18, P(S2) = 0.62, and P(S3) = 0.20. With sample information I, P(I | S1) = 0.12, P(I | S2) = 0.06, and P(I | S3) = 0.22. Compute the revised or posterior probabilities: P(S1 | I), P(S2 | I), and P(S3 | I). If required, round your answers to four decimal places.

State of Nature P (Sj|I)
S1 fill in the blank 1
S2 fill in the blank 2
S3 fill in the blank 3
Total Probability fill in the blank 4

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