Your question is Semi-Circle Random Points Probability. Take a moment with it on the right.
Talk me through your thinking if you like. When you're confident, submit your answer and I'll grade it like a real screen (7/10 or better passes).
If you generate n points at random locations on a circumference, what's the probability that all of the points will lie on the same semi-circle?
Assume the points are independently and uniformly distributed around the circumference, and that points exactly on a semicircle boundary have probability zero. Derive a closed-form expression in terms of n and evaluate it for the supplied example.
| Quantity | Value |
|---|---|
| Number of points, n | 8 |
| Simulation trials for verification | 1,000,000 |