perplexus.info :: Probability : Two random points

Two random points (Posted on 2018-04-26)

On a circumference of a given circle with a radius R two random points A & B are independently chosen.

What is the probability of AB being less than R ?

No Solution Yet Submitted by Ady TZIDON

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Solution

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For convenience create a coordinate system with the origin at the center of the circle and (1,0)=A

B is at some angle from -180 to 180 from A with uniform probability. AB is only closer than R if the angle is between -60 and 60.

Thus the probability is 120/360 = 1/3.

Posted by Jer on 2018-04-26 09:50:49

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