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Question

Points are selected at random inside the circle until a point is closer to the centre than to the circumference. What is the probability that exactly three points are selected?

A
932
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B
1664
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C
964
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D
None of the above
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Solution

The correct option is D 964
Let the radius of the circle be r. So the radius of points near to the center of circle will be r2. It is told that exactly 3 points are selected which are near to the center of the circle.
The radius for the three points =32.r2=3r4
Area of circle =π(3r4)24πr2
=9πr24πr2
=964.
Hence, the answer is 964.

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