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Random points in the unit circle

Source: IMC 2019 Day 2 P10

July 31, 2019
probabilitycollege contestsIMC

Problem Statement

20192019 points are chosen at random, independently, and distributed uniformly in the unit disc {(x,y)∈R2:x2+y2≤1}\{(x,y)\in\mathbb R^2: x^2+y^2\le 1\}. Let CC be the convex hull of the chosen points. Which probability is larger: that CC is a polygon with three vertices, or a polygon with four vertices?
Proposed by Fedor Petrov, St. Petersburg State University
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