Intersecting Chords

Probability Level 5

Two points are chosen uniformly at random on the unit circle and joined to make a chord C1C_1. This process is repeated 1717 more times to get chords C2,C3,,C18C_2, C_3, \ldots, C_{18}. What is the expected number of pairs of chords that intersect?

Details and assumptions

If kk chords intersect at the same point, this counts as (k2)\binom{k}{2} pairs of intersecting chords.

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