Compute the revised or posterior probabilities: P(S11), P(S2 ID) and P(S3 II). If required, round your answers to four decimal places.

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Problem 13-23 (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) = 0.22, P(S2) = 0.59 and P(53) = 0.19.
With sample information I, P(I | S1) = 0.15, P(I | S2) = 0.04 and P(I | S3) = 0.22.
Compute the revised or posterior probabilities: P(S1 | 1), P(S211) and P(S3 II). If
required, round your answers to four decimal places.
State of Nature
51
S
3₂
Sum
P(S) 17)
Transcribed Image Text:Problem 13-23 (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) = 0.22, P(S2) = 0.59 and P(53) = 0.19. With sample information I, P(I | S1) = 0.15, P(I | S2) = 0.04 and P(I | S3) = 0.22. Compute the revised or posterior probabilities: P(S1 | 1), P(S211) and P(S3 II). If required, round your answers to four decimal places. State of Nature 51 S 3₂ Sum P(S) 17)
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