Fred and Gina are playing tennis. The first player to win 2 sets wins their match. Fred has a 3/5 chance to win each set while Gina has a 2/5 chance. What is the probability that Fred wins the match?

A. 44/125

B. 63/125

C. 81/125

D. 62/125

Answer: C. 81/125

Step-by-step explanation:

The games is over in 3 sets. For Fred to win the match there are 3 possibilities.

1) Fred wins the first 2 sets with probability (3/5) ^2

2) Fred wins the first set. Looses the next set. Wins the third set.

(3/5) (2/5) (3/5)

3) Fred looses the first set. Wins the next 2 sets.

(2/5) (3/5) (3/5)

The probability that Fred wins is the sum of the above 3 probabilities. That means that the probability that Fred wins the match is

(3/5) ^2 + (3/5) ^ (2) (2/5) + (3/5) ^ (2) (2/5) = 81/125

Answer: it's answer c

Step-by-step explanation:81/125