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Two random points (Posted on 2018-04-26) Difficulty: 3 of 5
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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re(2): There must be a reason for the D3 rating. No. | Comment 7 of 10 |
(In reply to re: There must be a reason for the D3 rating. by Ady TZIDON)

Bertrand's Paradox is about picking a random chord and the problem that can arise from not defining how such a chord is to be determined.  If you choose different methods to define a random chord you can different results.


That does not apply here.  There is only one method of picking points on a circle that does not feel contrived: with a uniform distribution along the circumference which corresponds to a uniform distribution of the angle.  

If we try to get a Bertrand style paradox here, we might say that a random chord's endpoints are two random points.  But it's hard to justify calling them independent.

  Posted by Jer on 2018-04-26 14:44:33
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