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): Numerical Answers
It means what is the probability that all some diameter can be placed on the circle such that all the points thus far lie on one side of the diameter. For example, points at theta = -20, 20 and 150 degrees all lie on a span of 170 degrees and therefore is ok. If, however they were at -40, 20 and 150 degrees, that would be a span of 190 degrees and so count as a non-occurrence of what is sought.
Posted by Charlie
on 2003-05-19 15:40:22