Question

A point $p$ is selected randomly from the interior of the circle, then the probability that it is closer to the center of the circle rather than its boundary is :

• A. $\frac{1}{3}$
• B. $\frac{2}{3}$
• C. $\frac{1}{4}$
• D. $\frac{3}{4}$

Answer 1

The correct option is C $\frac{1}{4}$

For a point to be closer to the center than the boundary , the point must lie in the region between center and half of the radius of the circle.
Required probability $=\frac{\pi {\left(\frac{r}{2}\right)}^2}{\pi r^2}=\frac{1}{4}$