Chapter 8.3, Problem 8.52E

To determine

To calculate the probability that exactly threeof six friends win a prize.

Answer to Problem 8.52E

  $0.05358$

Explanation of Solution

Given:

  $\begin{array}{l}n=6\\ p=\frac{1}{6}\end{array}$

The binomial probability:

  $P(X=k)=C{}_k\times p^k\times {(1-p)}^{n-k}$

Evaluate at $k=3$ :

  $\begin{array}{l}$ P(X=3)=C{}_3\times {(\frac{1}{6})}^3\times {(1-\frac{1}{6})}^{6-3}$$ =20\times {(\frac{1}{6})}^3\times {(\frac{5}{6})}^3$=\frac{625}{11664}\\ =0.05358\end{array}$