Chapter 13, Problem 10SAP

To determine

To find: The probability that dart will land on the shaded region.

Answer to Problem 10SAP

Therequired probability is $\frac{3}{4}$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

Calculation:

Consider the ratio of the area of the shaded region to the unshaded region is,

  $P=\frac{\pi r^2-\pi r_2^1}{\pi r^2}$

Then,

  $\begin{array}{c}P=\frac{\pi {\left(2\right)}^2-\pi {\left(1\right)}_2^1}{\pi {\left(2\right)}^2}\\ =\frac{4-1}{4}\\ =\frac{3}{4}\end{array}$

Thus, the required probability is $\frac{3}{4}$ .