Chapter 13, Problem 9PT

To determine

Find the probability for which the person will shoot the shaded region as shown in figure below.

  

Answer to Problem 9PT

The probability of shaded region is $\frac{4}{25}$ .

Explanation of Solution

Given information: The given figure is shown as,

  

Calculation: From the geometric probability concept, the probability $P\left(\text{shaded region}\right)$ of shaded region is evaluated as,

  $\begin{array}{c}P\left(\text{shaded region}\right)=\frac{\text{Area of shaded region}}{\text{Area of total region}}\\ =\frac{\pi {\left(2\right)}^2}{\pi {\left(5\right)}^2}\\ =\frac{4}{25}\end{array}$

Hence the probability of shaded region is $\frac{4}{25}$ .