Probability of a deuce in tennis?
In a game of tennis, if one player gets 4 points and the other has 2 or fewer, the game is over. However, if both players get 3 points, this is called a Deuce and the game continues until one player has 2 more points than the other.
Suppose two players are equally skilled (i.e. have an equal chance of winning each round), Find , where is the probability of them reaching a deuce.
Details and Assumptions :
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Both players start with 0 points.
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The winner of each round gets 1 point added to their score when the round is over. There are no draws in tennis.
The answer is 3125.
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1 solution
In order to get to a deuce, 6 points must be played, and exactly 3 must be won by each player. Each point can turn out one of two ways - either one player wins or the other wins. Thus there are 2 6 = 6 4 ways that the 6 points can turn out. The number of possible ways for each player to win three games is ( 3 6 ) = 2 0 . Since each point is equally likely to be won by either player, the probability of reaching a deuce is p = 6 4 2 0 = 1 6 5 = 0 . 3 1 2 5 . Thus 1 0 0 0 0 p = 3 1 2 5 .