Pick two points at random on a circle and draw the chord connecting them.
Pick two more points and connect them with a second chord.
What is the probability that these chords intersect?
(In reply to
re(2): solution, maybe by Charlie)
Solutions that work for a circle do not apply to a square.
I think the circle solution does apply to any convex shape, even irregular ones, even ones with corners, as long as no part of its' edge is a straight line.
If the shape has a straight line, then there is a problem when all four points lie on the same straight line. When all four points lie on a straight line, then there is a 2/3 probability that the "chords" "intersect" (i.e, share points in common).
In the case of the square, there is a 1/64 chance that all 4 points lie on the same edge. Therefore, the probability that the chords intersect (share points in common) on a square is (1/3)*(63/64) + (2/3)*(1/64) = 65/192
Edited on May 13, 2009, 3:28 pm
re(3): solution, maybe
