Suppose that you are given a decision situation with three possible states of nature S 1 , S 2 , and S 3 The prior probabilities are P ( S 1 ) 0 22, P ( S 2 ) 0 59, and P ( S 3 ) 0 19 With sample information I , P ( I S 1 ) 0 15, P ( I S 2 ) 0 04, and P ( I S 3 ) 0 22 Compute the revised or posterior probabilities P ( S 1 I ), P ( S 2 I ), and P ( S 3 I ) If required, round your answers to four decimal places State of Nature P ( S j I ) S 1 S 2 S 3

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Question: Suppose that you are given a decision situation with three possible states of nature: S 1 , S 2 , and S 3 . The

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(S₃) = 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 | I), P(S₂ | I), and P(S₃ | I). If required, round your answers to four decimal places.

State of Nature	P (S_j\|I)
S₁
S₂
S₃

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