Two pairs of points are randomly chosen on a circle. Find the probability that the line joining the two points in one pair intersects that in the other pair.

I've been thinking over this problem, assuming one pair and finding that the other pair has to be entirely in one of the two arcs of the circle that the first pair of points divides it into.

But I've not been able to find an explicit answer. If I assume one point to be (a,b), I'm not able to manage the other three points.

I've been thinking over this problem, assuming one pair and finding that the other pair has to be entirely in one of the two arcs of the circle that the first pair of points divides it into.

But I've not been able to find an explicit answer. If I assume one point to be (a,b), I'm not able to manage the other three points.