Chapter 6.7, Problem 16E

To determine

To find : the probability that the ring in the searched section.

Answer to Problem 16E

The probability that the ring is in the searched section of the field is $\frac{16}{\text{143}}$ .

Explanation of Solution

Given information :

The dimension of the rectangular field is 110 yards by 65 yards and 25 yards by 32 yards have been searched.

Calculation :

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

  $\begin{array}{l}\text{Area of rectangular field}=110\times 65\\ \text{Area of rectangular field}=7,150\text{ sq yards}\end{array}$

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

  $\begin{array}{l}\text{Area of rectangular field searched}=25\times 32\\ \text{Area of rectangular field searched}=800\text{ sq yards}\end{array}$

Thus, the probability that the ring is in the searched section is

  $\begin{array}{l}P\left(\text{Ring in searched section}\right)=\frac{\text{Number of success}}{\text{Number of trials}}\\ P\left(\text{Ring in searched section}\right)=\frac{800}{\text{7150}}\\ P\left(\text{Ring in searched section}\right)=\frac{16}{\text{143}}\end{array}$

Hence,

The probability that the ring is in the searched section of the field is $\frac{16}{\text{143}}$ .