Consider a decision situation with four possible states of nature: s₁, s₂, s₃, and s₄. The prior probabilities are P(s₁) = 0.35, P(s₂) = 0.15, P(s₃) = 0.20, P(s₄) = 0.30. The conditional probabilities are P(C|s₁) = 0.2, P(C|s₂) = 0.09, P(C|s₃) = 0.15, and P(C|s₄) = 0.20. Find the revised (posterior) probabilities P(s₁|C), P(s₂|C), P(s₃|C), and P(s₄|C).

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The Answer of Consider a decision situation with four possible states of nature: s₁, s₂, s₃, and s₄. The prior probabilities are P(s₁) = 0.35, P(s₂) = 0.15, P(s₃) = 0.20, P(s₄) = 0.30. The conditional probabilities are P(C|s₁) = 0.2, P(C|s₂) = 0.09, P(C|s₃) = 0.15, and P(C|s₄) = 0.20. Find the revised (posterior) probabilities P(s₁|C), P(s₂|C), P(s₃|C), and P(s₄|C).

Consider a Decision Situation with Four Possible States of Nature