Chapter 4.4, Problem 65AYU

Tennis Anyone? 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

$p\left(x\right)=\frac{x^4\left(-8x^3+28x^2-34x+15\right)}{2x^2-2x+1}$

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.

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 $0.64$?

Find and interpret $p\left(0.64\right)$

Solve $p\left(x\right)=0.9$.

Graph $p=p\left(x\right)$ for $0\le x\le 1$. Describe what happens to $P$ as $x$ approaches $1$.