Four points J, K, L, and M are chosen at random on the circumference of a circle. What is the probability that chord JK and chord LM intersect?
"Anchor" J at any point on the circumference
Proceeding in a clock-wise direction we could have the following possibilities for the four points
Note that the two entries in red are the ones where chords JK and LM intersect
So.....the probability of intersecting chords is 2 / 6 = 1 / 3