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.

Question

asked Jan 25, 2021 107k views

1 Answer

Ryun · Answer 1 · 2021-01-30T05:53:01+0000

Answer:0.25

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
(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

$P=(\pir^2)/(\pi R^2)$

$P=(\pi (0.5R)^2)/(\pi R^2)$

P=(1)/(4)