Four points on a semicircle
Four points are dropped independently and uniformly at random on the circumference of a circle. What is the probability that all four lie within some common semicircle? (to 3 decimals)
Show hints (2)+
- Anchor the semicircle to a "leader" point that has all the others clockwise within - and argue the leader is unique.
- A fixed point is the leader with probability ; sum over the four disjoint leaders.
Answer
Reveal answer →Final answer
0.5 (± 0.001)
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