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(3): Simulation by DJ)

In all 10000 trials 3 random points all three fell within a 180° span? And with 4 points, 8742 out of 10000 fell within the span, when 5000 would have been expected? If 5000 are expected we'd usually expect that number +/- 70 as the standard deviation, so even 3 std deviations would be 5210--nowhere near 8742.

Posted by Charlie on 2003-05-22 05:25:35