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 ?

(In reply to

There must be a reason for the D3 rating. by Charlie)

Ch

You are right to perceive that the solution depends on the way of generating the random points and therefore distinct simulations will result in a wide range of distinct answers.

Please read about Bertrandâ€™s paradox- there are several related papers on the web - and then sum up your comments upon the text of the puzzle.

This is one of many problems that do not offer a clear-cut solution without a-priori assumptions.

BTW I am on vacation in Cyprus and sending my comment from my smartphone - a tedious job taking in account the size of my fingers

Still I wanted to justify my resistance to the d1 label...