Question

Problem 3. In the game of tennis, the first player to win four points wins the game as long as the winner's total is at least two points more than the opponent. Thus if the game is tied at 3-3(Deuce"), then the game is not decided by the next point, but must go on until one player has two points more than the opponent's score. Assume that the server has a constant probability p of winning each point, independently of the outcomes of any other points. a) If the score is currently at Deuce, then find the probability that the server wins the game. (Your answer will be a function of p) b) Find the probability that the server wins a game from the start, starting witlh a score of 00. Note that there are several different ways that a player can win: She can win in four points straight, with a score of 4-0, or in five points with a score of 4-1, or in six points with a score of 4-2, or by winning Deuce c) Use a computer or graphing calculator to plot a graph of the player's game-win probability found in part b), as a function of p. Decide whether your plot makes sense d) If the server loses about a third of his points, on average, then what percentage of his games will he lose?

Answer 1