CBSE - XII Science - Mathematics - Probability
The solution of your problem is as follows -
Consider a circle of radius R, then a randomly chosen point would be closer to centre than the circumference if it lies in a circle with same centre but of radius R/2 (as shown in the figure).
P(point closer to center than circumference) = Area of shaded region (circle with radius R/2) / Area of the circle with radius R
=> P(point closer to center than circumference) = π(R/2)2 / π(R)2
= π(R)2 / 4π(R)2
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