Suppose that you are given a decision situation with three possible states of nature: s1, s2, and s3. the prior probabilities are p(s1) = 0.16, p(s2) = 0.57, and p(s3) = 0.27. with sample information i, p(i | s1) = 0.13, p(i | s2) = 0.07, and p(i | s3) = 0.19. 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.