Intersecting Chords

Two points are chosen uniformly at random on the unit circle and joined to make a chord \(C_1\). This process is repeated \(17\) more times to get chords \(C_2, C_3, \ldots, C_{18}\). What is the expected number of pairs of chords that intersect?

Details and assumptions

If \(k\) chords intersect at the same point, this counts as \(\binom{k}{2}\) pairs of intersecting chords.

×

Problem Loading...

Note Loading...

Set Loading...