Question

A point is selected at random inside a circle. Find the probability that the point is closer to the center of the circle than to its circumference.

Answer 1

Answer:0.25

Step-by-step explanation:

Suppose a circle of Radius R

Points which are near to the circle will lie in the vicinity of center up to a distance r

r should be equal to $\frac{R}{2}$ i.e. beyond 0.5 R points are away from the center and inside 0.5 R it is closer to center

Probability of finding a point closer to the circle is

$P=\frac{\pir^2}{\pi R^2}$

$P=\frac{\pi (0.5R)^2}{\pi R^2}$

$P=\frac{1}{4}$