Chapter 11, Problem 23CR

To determine

To Find: The probability that the point is inside the smaller circle.

Answer to Problem 23CR

  $\frac{9}{25}$

Explanation of Solution

Given: A point is randomly chosen inside a larger circle.

  

Radius of circles.

  $\begin{array}{l}{R}_s=3\\ R_l=5\\ Area\\ A_s=\pi r^2\\ $ A_s=\pi {(3)}^2$A_s=9\pi \\ similarly\\ A_l=\pi r^2\\ $ A_l=\pi {(5)}^2$A_l=25\pi \end{array}$

Then

Probability that the point is inside the smaller circle.

  $P=\frac{A_s}{A_l}=\frac{9\pi }{25\pi }=\frac{9}{25}$

Hence, the probability is$\frac{9}{25}$.