Kim and Susan are playing a tennis match where the winner must win 2 sets in order to win the match. For each set the probability that Kim wins is 0.64. The probability of Kim winning the set is not affected by who has won any previous sets. (a) What is the probability that Kim wins the match? (b) What is the probability that Kim wins the match in exactly 2 sets (i. e. only 2 sets are played and Kim is the one who ends up winning) ? (c) What is the probability that 3 sets are played?

a) the probability that Kim wins the match is 0.7046

b) the probability that Kim wins the match in exactly 2 sets is 0.4096

c) the probability that 3 sets are played is 0.4608

Step-by-step explanation:

a) Kim's wins:

P (Kim wins first two sets) = 0.64*0.64=0.4096 P (Kim wins first set, Susan wins second set, Kim wins third set) = 0.64*0.36*0.64≈0.1475 P (Susan wins first set, Kim wins second and third set) = 0.36*0.64*0.64≈0.1475

P (Kim wins) = 0.4096+0.1475+0.1475=0.7046

b) Kim wins the match in exactly 2 sets

P (Kim wins first two sets) = 0.64*0.64=0.4096

c) 3 sets are played

P (Kim wins first set, Susan wins second set, Kim wins third set) = 0.64*0.36*0.64≈0.1475

P (Susan wins first set, Kim wins second and third set) = 0.36*0.64*0.64≈0.1475

P (Kim wins first set, Susan wins second and third set) = 0.64*0.36*0.36≈0.0829

P (Susan wins first set, Kim wins second set and Susan wins third set) = 0.36*0.64*0.36≈0.0829

P (3 sets are played) = 0.1475+0.1475+0.0829+0.0829=0.4608