Chapter 6.7, Problem 17E

To determine

To find : the chance that the chest is in the searched region.

Answer to Problem 17E

The chance that the chest is in the searched region is $\frac{1}{\text{24}}$ .

Explanation of Solution

Given information :

Consider, the information provided in the question,

The dimension of the rectangular field is 100 by 60 feet and 25 square feet have been searched.

Calculation :

Here, total number of trials is the area of the rectangular field.

  $\begin{array}{l}\text{Area of rectangular field}=100\times 60\\ \text{Area of rectangular field}=6,000\text{ square feet}\end{array}$

Also, the number of success is the area of field that is searched. Therefore,

  $\text{Area of rectangular field searched}=25\text{ square feet}$

Thus, the probability that the chest is in the searched region is

  $\begin{array}{l}P\left(\text{Chest in searched region}\right)=\frac{\text{Number of success}}{\text{Number of trials}}\\ P\left(\text{Chest in searched region}\right)=\frac{25}{\text{600}}\\ P\left(\text{Chest in searched region}\right)=\frac{1}{\text{24}}\end{array}$

Hence,

The chance that the chest is in the searched region is $\frac{1}{\text{24}}$ .