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pow:problem6s22

Problem 6 (due on Monday, April 25)

$n$ points are chosen randomly and independently on a circle, each with the uniform distribution. What is the probability that all $n$ points are contained in some closed semicircle?

We received only one solution, from Prof. Vladislav Kargin. His solution is the same as our “in-house” solution. The probability in question is $\frac{n}{2^{n-1}}$. For a justification and more details see the following link Solution.