Problem 5 (10 pts) Tom has an opportunity to place a bet on the outcome of an upcoming horse racing and he is interested in betting on the horse named Bay. Suppose Tom starts with the initial wealth Wo. If Tom bets a dollars and Bay wins, Tom will get Wo +a in the end. On the other hand, if Bay loses, Tom will have Wo - a left. Suppose that Tom only knows that each race horse is of type A or type B. Type A has 80% chance to win and type B has 50% chance to win. After all the buzz that Tom has been hearing, he is 90% sure that Bay is of type A and 10% that Bay is of type B. Suppose that Tom currently has the utility preference U (x) = In(x), what fraction of the initial wealth will Tom bet on the horse Bay (i.e. a*/W.)