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 2003-05-19 15:44:21