Given n points drawn randomly on the circumference of a circle, what is the probability they will all be within any common semicircle?
(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 20030521 19:23:55 