2005 Putnam A6

Let $n$ be given, $n \geq 4$, and suppose that $P_1, P_2, \dots, P_n$

are $n$ randomly, independently and uniformly, chosen points on a circle.

Consider the convex $n$-gon whose vertices are the $P_i$. What is the

probability that at least one of the vertex angles of this polygon is

acute?

给定 $n$，$n \geq 4$，并假设 $P_1, P_2, \dots, P_n$

是圆上随机、独立且均匀地选择的 $n$ 个点。

考虑凸 $n$ 边形，其顶点为 $P_i$。什么是

该多边形至少有一个顶角为的概率

急性？