=d. A famous football guru, William Walsh, has offered his services to help evaluate whether the team will have a winning season. For $100,000, he will carefully evaluate the team throughout spring practice and then throughout preseason workouts. William then will provide his prediction on September 1 regarding what kind of season, W or L, the team will have. In similar situations in the past when evaluating teams that have winning seasons 50 percent of the time, his predictions have been correct 75 percent of the time. Considering that this team has more of a winning tradition, if William predicts a winning season, what is the posterior probability that the team actually will have a winning season? What is the posterior probability of a losing season? If William predicts a losing season instead, what is the posterior probability of a winning season? Of a losing season?

Show how these answers are obtained from a probability tree diagram.