1. Suppose that you are given a decision situation with three possible states of nature: S₁, S₂, and S₃. The prior probabilities are P(S₁) = 0.21, P(S₂) = 0.48, and P(S₃) = 0.31. With sample information I, P(I | S₁) = 0.12, P(I | S₂) = 0.05, and P(I | S₃) = 0.20. 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) S₁S₂S₃

_{Can you please help me find the states of nature and the way to solve the problem. I'm having a hard time with this.}