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 Am I correct in saying this by sendil)

The second point might be less than 180 degrees from the first. Say it's 50 degrees away from the first. Then an entire span of 360 - 50 = 310 is OK to continue within one semicircle (the central 50 degrees plus 130 degrees on either side). So the probability depends on the whole probability distribution of the previous number of points, and after the third point plotted, the distribution is not even uniform.

Posted by Charlie on 2003-05-20 04:53:19