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Don't Be a Square (Posted on 2003-05-19) Difficulty: 4 of 5
Given n points drawn randomly on the circumference of a circle, what is the probability they will all be within any common semicircle?

See The Solution Submitted by DJ    
Rating: 4.4667 (15 votes)

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re(3): Simulation | Comment 17 of 21 |
(In reply to re(2): Simulation by Charlie)

I found a simulation someone else had done, with 10000 samples per n, with the fraction of the time that all n points were within the same 180° arc. The table looked like this:
 n    simulation     
 1      1.0000
 2      1.0000
 3      1.0000
 4      0.8742
 5      0.6862
 6      0.4954
 7      0.3365
 8      0.2295
 9      0.1508
10      0.0889
I didn't run that myself; that's just what I found. Anyway, it corresponds pretty well to the solution.
  Posted by DJ on 2003-05-21 19:23:55

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