Chapter 6.3, Problem 115E

To determine

To find: The probability that Jeff will play exactly 5 times.

Answer to Problem 115E

The probability is ${0.25}^5$ .

Explanation of Solution

Given:

Number of trials ( n ) = 4

Probability of success $\left(p\right)=\frac{1}{4}=0.25$

Calculation:

Consider, X is a random variable that depicts the number of games that are won follows the binomial distribution with n = 4 and p = 0.25.

The probability that Jeff will play exactly 5 timescan be calculated as:

  $\begin{array}{c}P\left(X=5\right)=\left(\begin{array}{c}5\\ 5\end{array}\right){\left(0.25\right)}^5{\left(1-0.25\right)}^{5-5}\\ =1\times {\left(0.25\right)}^5\times {\left(1-0.25\right)}^0\\ ={0.25}^5\end{array}$

Thus, the required probability is ${0.25}^5$ .

Hence, the correct option is (a).