Consider a tennis match with 3 sets . The first player to win 2 sets wins the match. Let the probability of winning a set be 0.3 (i. e. the probability of losing a set is 0.7). The winner of the tennis match gets $40, and the loser pays $40. Required:

a. Is this game recursive?
b. Draw and properly label the game tree. If there is a state that recurs, do not go beyond that state.
c. What is the value of the game in the state where both players have won 1 set each?
d. What is the probability of:
i. Winning the match
ii. Winning the match after winning the first set.
e. What is the value of the entire game?