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?

mathmathj28 Feb 11, 2020

#1**+2 **

"Anchor" J at any point on the circumference

Proceeding in a clock-wise direction we could have the following possibilities for the four points

JKLM

JKML

JLKM

JLMK

JMLK

JMKL

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

CPhill Feb 11, 2020