Chapter 13.4, Problem 24E

To determine

To find the probability that the football team will win its next four games.

Answer to Problem 24E

  $\frac{256}{2401}$

Explanation of Solution

Given:

The odds of winning each game are $4$ to $3$ .

Calculation:

Let $A$ be the event of winning the game.

Let $B$ be the event of losing the game.

Therefore probability of event $A$ is $P(A)=\frac{4}{7}$

And probability of event $B$ is $P(B)=\frac{3}{7}$

Hence,

  $\begin{array}{l}P(\text{winning 4 games})=P(A)\times P(A)\times P(A)\times P(A)\\ P(\text{winning 4 games})=\frac{4}{7}\times \frac{4}{7}\times \frac{4}{7}\times \frac{4}{7}=\frac{256}{2401}\end{array}$