MSELFtest 23. Suppose that you are given a decision situation with three possible states of nature: 81, 82, and 83. The prior probabilities are P(s₁) = 0.2, P(82) = 0.5, and P(83) = 0.3. With sample information I, P(I | s₁) = 0.1, P(I|s2) = 0.05 , and P(I|83) = 0.2. Compute the revised or posterior probabilities: P(s₁|I), P(82|I), and P(831).

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SELFtest
23. Suppose that you are given a decision situation with three
, 82,
possible states of nature: $₁, and 83. . The prior probabilities are P(s₁) = 0.2,
P(82) = 0.5, and P(83) = 0.3. With sample information I, P(I|s₁) = 0.1, P(I| s2) = 0.05
and P(I | 83) = 0.2. Compute the revised or posterior probabilities: P(s1|I), P(s2|I),
and P(s3|I).
Transcribed Image Text:SELFtest 23. Suppose that you are given a decision situation with three , 82, possible states of nature: $₁, and 83. . The prior probabilities are P(s₁) = 0.2, P(82) = 0.5, and P(83) = 0.3. With sample information I, P(I|s₁) = 0.1, P(I| s2) = 0.05 and P(I | 83) = 0.2. Compute the revised or posterior probabilities: P(s1|I), P(s2|I), and P(s3|I).
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23)  Answer:- Given, The prior probabilities are P(s1) = 0.2 , P(s2) = 0.5 , and P(3) = 0.3 . With sample information I, P(I | s1) = 0.1,    P(I | s2) = 0.05 and P(I | s3) = 0.2. 

Using formula, 

P(B|A) = [P(A|B)*P(A)]÷ [P(A|B)*P(A) ]

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