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
My idea as well by Gamer)
If the first point happens to be 0 degrees (or define 0 degrees as where the first point falls), and the second at say 30 degrees, then the third has to be between 0 and 180 or between 0 and 150. The only way for the test to fail if the first two were as stated would be for the third point to be between 150 and 180 (that is between 180 and 210, the same thing). So that particular case is not 1/2, but 30/360 = 1/12 of failing, or 11/12 of passing.

Posted by Charlie
on 20030519 15:44:21 