Chords that don't cross
Six points are placed uniformly at random on a circle, then split into three pairs and a chord is drawn for each pair. Assuming the three pairs are formed uniformly at random, what is the probability that none of the three chords intersect?
Show hints (2)+
- Positions don't matter - only the pairing does. There are pairings of points.
- Non-crossing pairings are Catalan-many: , so the probability is .
Answer
Reveal answer →Final answer
0.3333 (± 0.005)
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