Chapter 6.3, Problem 81E

To determine

To find: The $P\left(X=4\right)$ and interpret it.

Answer to Problem 81E

The probability is 0.2304

Explanation of Solution

Given:

Number of trials ( n ) = 7

Probability of success ( p ) = 0.44

Formula used:

The formula to compute the binomial probability is:

  $P\left(X=r\right){=}^n{C}_r\times p^r\times {\left(1-p\right)}^{n-r}$

Here.

  $\begin{array}{l}r\text{ is the number of successes}\\ n\text{ is the number of trials}\\ p\text{ is the probability of success}\end{array}$

Calculation:

  $P\left(X=4\right)$ can be calculated as:

  $\begin{array}{c}P\left(X=4\right){=}^7{C}_4\times {\left(0.44\right)}^4\times {\left(1-0.44\right)}^{7-4}\\ =0.2304\end{array}$

Thus, the required probability is 0.2304.

Interpretation:

The probability of selecting 4 out of 7 elks that survive to childhood is 23.04%.