Chapter 12, Problem 37SGR

To determine

The probability of the given statement for exactly successes.

Answer to Problem 37SGR

The probability is 0.2150.

Explanation of Solution

Given:

The binomial distribution has 40% rate of success.

There are 10 trails.

The binomial distribution is given as follows:

  $\begin{array}{l}P\left(X=x\right)=\left(\begin{array}{l}n\\ x\end{array}\right){\left(p\right)}^x{\left(1-p\right)}^{n-x}\\ \text{Substituting the known values:}\\ P\left(X=x\right)=\left(\begin{array}{l}10\\ 3\end{array}\right){\left(0.4\right)}^3{\left(1-0.4\right)}^{10-3}\\ =\left(\begin{array}{l}10\\ 3\end{array}\right){\left(0.4\right)}^3{\left(0.6\right)}^{10-3}\\ =0.2150\end{array}$

Therefore, the probability of exactly 3 success is,

  $P\left(X=3\right)=0.2150$

Therefore, the required probability is 0.2150.