Expected chord intersections
Ten chords of a circle are drawn, each defined by two independent uniformly random points on the circle (all endpoints distinct). What is the expected number of intersection points among the chords (inside the circle)?
Show hints (2)+
- Two chords cross iff their endpoints alternate around the circle - probability for a random pair.
- Use linearity of expectation over pairs.
Answer
Reveal answer →Final answer
15
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