A tennis match requires that a player win three of five sets to win the match. If a player wins the first two sets,what is the probability that the player wins the match,assuming that each player is equally likely to win each set?
A)0.500
B)0.125
C)0.875
D)0.000

Question

Quizplus · Accepted Answer

The player needs to win one more set out of the remaining three sets to win the match. Since both players are equally likely to win each set, the probability of the player winning a set is 1/2. Therefore, the probability of the player winning the next set is 1/2. The probability of the player losing the next set is also 1/2. If the player loses the next set, then the match is tied at 2-2 and it goes to the final set where either player can win. Therefore, the probability of the player winning the match is the probability of either winning the next set or winning the final set if it goes to 2-2. This can be calculated as follows:
P(player wins match) = P(player wins next set) + P(match goes to 2-2 and player wins final set)
P(player wins match) = (1/2) + (1/2)*(1/2) = 3/4 = 0.875
Therefore, the correct answer is (C) 0.875.

A Tennis Match Requires That a Player Win Three of Five