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A6

Part of 2005 Putnam

Problems(1)

Putnam 2005 A6

Source:

12/5/2005
Let nn be given, n≥4,n\ge 4, and suppose that P1,P2,…,PnP_1,P_2,\dots,P_n are nn randomly, independently and uniformly, chosen points on a circle. Consider the convex nn-gon whose vertices are the Pi.P_i. What is the probability that at least one of the vertex angles of this polygon is acute.?
Putnamprobabilitycalculusfunctionintegrationgeometrygeometric transformation