Question

Baby elk Refer to Exercise 77 . Use the binomial probability formula to find P(X = 4) . Interpret this value.

Short answer

The chance of picking 4 out of 7 elks who live to be children is$\text{23.04\%}$

Step-by-step solution

Step 1:Given Information

The total number of trials $\mathrm{n}=7$

The likelihood of success $\left(\mathrm{p}\right)=0.44$

The binomial probability is calculated using the following formula:

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

Furthermore,

The number of successes is r in this case.

The number of trials is n.

The chance of success is denoted by p.

Step 2:Simplificaiton

$\mathrm{P}\left(\mathrm{X}=4\right)$can be computed as follows:

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

As a result, the necessary probability is $0.2304$

The chance of picking 4 out of 7 elks who live to be children is $23.04\%$