Book Problem 4-23 (Algorithmic) Suppose that you are given a decision situation with three possible states of nature: $1, Sz, and $3. The prior probabilities are P($1) = 0. 17, P($2) = 0.53, and P(S3) = 0.30. With sample information I, P(I | $1) = 0.13, P(I | $2) = 0.04, and P(1 ( $3) = 0.19. Compute the revised or posterior probabilities: P(51 | 1), P(S2 | !), and P(S3 | I). If required, round your answers to four decimal places. State of Nature P (SID) $1 S2 $3 Total Probability