Chapter 6.3, Problem 114E

To determine

To find: The probability that Jeff will win exactly 1 prize.

Answer to Problem 114E

The probability is $\left(\begin{array}{c}4\\ 1\end{array}\right){\left(0.25\right)}^1{\left(1-0.25\right)}^3$ .

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 win exactly 1 prize can be calculated as:

  $\begin{array}{c}P\left(X=1\right)=\left(\begin{array}{c}4\\ 1\end{array}\right){\left(0.25\right)}^1{\left(1-0.25\right)}^{4-1}\\ =\left(\begin{array}{c}4\\ 1\end{array}\right){\left(0.25\right)}^1{\left(1-0.25\right)}^3\end{array}$

Thus, the required probability is $\left(\begin{array}{c}4\\ 1\end{array}\right){\left(0.25\right)}^1{\left(1-0.25\right)}^3$ .