3. In women's tennis, a player must win 2 out of 3 sets to win a match. If a player wins the first 2 sets, she wins the match and the third set is not played. Player V and Player M will compete in a match. (a) Let V represent the event that player V wins a set, and let M represent the event that Player M wins a set. (i) List all possible sequences of events V and M by set played that will result in Player V winning the match. ii) List all possible sequences of events V and M by set played that will result in Player M winning the match. MM Player V and Player M have competed against each other many times. Historical data show that each player is equally likely to win the first set. If player V wins the first set, the probability that she will win the second set is 0.60. If Player V loses the first set, the probability that she will lose the second set is 0.70. If Player V wins exactly one of the first two sets, the probability that she will win the third set is 0.45. (b) What is the probability that Player V will win a match against Player M? one 3rd (c) What is the probability that a match between Player V and Player M will consist of 3 sets given that Player V wins the match? Mr (d) What is the expected number of sets played when Player V competes in a match with Player M? KE favernd