Posterior probabilities are conditional probabilities based on the outcome of the sample information. These can be computed by developing a table using the following process. Enter the states of nature in the first column, the prior probabilities for the states of nature, P(I|sj), in the second column and the conditional probabilities in the third column. In column 4 compute the joint probabilities by multiplying the prior probability values in column 2 by the corresponding conditional probabilities in column 3. Sum the joint probabilities in column 4 to obtain the probability of the sample information I, P(I). In column 5, divide each joint probability in column 4 by P(I) to obtain the posterior probabilities, P(sj|I). The prior probabilities are given to be P(s1) = 0.4, P(s2) = 0.5, and P(s3) = 0.1. The conditional probabilities given each state of nature are P(I|s1) = 0.1, P(I|s2) = 0.05, and P(I|s3) = 0.2