Q4. Suppose St. Marys University is about to play AAU for tennis championship. The St, Marys team has two players (A and B), and the IAAU team has three players (X, Y, and Z). The following facts are known about the players relative abilities: X will always beat B; Y will always beat A; A will always beat Z. In any other match, each player has a 12 chance of winning. Before St. Mary plays AAU, the St. Marys coach must determine who will play first singles and who will play second singles. The AAU coach (after choosing which two players will play singles) must also determine who will play first singles and second singles. Assume that each coach wants to maximize the expected number of singles matches won by the team. Use game theory to determine optimal strategies for each coach and the value of the game to each team.