Question

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 the match goes three sets until someone wins?

Answer 1

60/125 which can be reduced to 12/25

Explanation:

Gina wins

2/5 * 2/5 = 4/25

3/5 * 2*5 * 2/5 = 12 /125

2/5 * 3/5 * 2/5 = 12/125

Fred Wins

3/5 * 3/5 = 9/25

2/5 * 3/5 * 3/5 = 18/125

3/5 * 2/5 * 3/5 = 18/125

P(3 sets) = (18 + 18 + 12 + 12)/125 = 60/125

P(2 sets) = (20 + 45)/125 = 65/125

I found the probability of 2 sets so I could add the results together to see if the probability totals 1. It does. This question is done correctly.