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?

let a be the length of the shorter arc made by the chord and let the radius of the circle be 1.  Now the odds of the second chord intersecting is c*(2*pi-c)/(4*pi^2).  So to get the total probability we simply take

(1/(4*pi^2))*¡Òc*(2*pi-c) dc with c ranging from 0 to pi.  And computing this we get pi/6 so the odds of them intersecting is

pi/6¡Ö0.5326 or 53.26%

Posted by Daniel on 2009-05-11 12:03:38