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 match?
A) 0.5
B) ⅛ or 0.125
C) ⅞ or 0.875
D) Cannot be computed.

Question

Quizplus · Accepted Answer

If the player wins the third set, then they win the match. If they lose the third set, then they must win the fourth and fifth sets to win the match. Since both players are equally likely to win each set, the probability of winning the third set is 0.5. If they lose the third set, the probability of winning two more sets in a row is (0.5)^2 = 0.25. So the overall probability of winning the match is 0.5 + (0.5)(0.25) = 0.875 or ⅞.

A Tennis Match Requires That a Player Win Three of Five