To win a game in tennis, a player must win four points. If both players have won three points, the play continues until a player is ahead by two points to win the game. The model

represents the probability P of a player winning a game in which the player is serving the game and x is the probability of winning a point on serve. The player serving is the first to put the ball in play.

(a) What is the probability that a player who is serving will win the game if the probability of the player winning a point on serve is 0.64?

(b) Find and interpret P(0.62).

(c) Solve P(x) = 0.9.

(d) Graph P = P(x) for 0 ≤ x ≤ 1. Describe what happens to P as x approaches 1.

Transcribed Image Text:

P(x): = x4 (-8x³ + 28x² - 34x+15) 2x² - 2x + 1