Question

A ball is thrown at a circular bin such that it will land randomly over the area of the bin. Find the probability that it lands closer to the center than to the edge?

(a) 51%

(b) 25%

(c) 72%

(d) 34%

I had been asked this question in an interview.

My doubt stems from Geometric Probability in chapter Discrete Probability of Discrete Mathematics

Answer 1

The correct option is (b) 25%

Explanation: The set of outcomes are all of the points on the bin, which make up an area of where is the radius of the circle. The points which are closer to the center than to the edge are those that lie within the circle of radius around the center. Hence, the area of the success outcomes is π(r/2)^2 = πr^2/4. Thus, P(closer to center than edge)=(area of the desired outcome)/(area of the total outcome) = πr^2/4 /πr^2 = 1/4 = 0.25 = 25%.