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?

Once drawn the first chord, trace the diameter that is the median of this chord. Once chosen randomly the third point, there is a probability of 50% of choose the fourth point at the same side (relatively to the traced diameter) and 50% at the other side. In the first case, the lines will not cross, and in the second, they will cross. So, the asked probability is 50%.  

Posted by pcbouhid on 2009-05-11 17:21:38