Four points A1, A2, A3 and A4 are chosen at random on a circle. Find the probability that chords A1A2 and A3A4 intersect.
Out of 4 ways, there is only one way to set up the chords so that A_1 A_2 and A_3 A_4 intersect, so the probability is 1/4.
"Anchor" A1 at any point on the circle
Moving clock-wise.....we have the following possible configurations
A1 A2 A3 A4
A1 A2 A4 A3
A1 A3 A2 A4
A1 A3 A4 A2
A1 A4 A2 A3
A1 A4 A3 A2
Note that onlt 2 of the 6 possibilites have chord A1 A2 intersecting chord A3 A4
So....the probability is 2 / 6 = 1 / 3