IMC 2019 · Problem 10

2019 points are chosen at random, independently, and distributed uniformly in the unit disc $\{(x, y) \in \mathbb{R}^2 : x^2 + y^2 \le 1\}$. Let $C$ be the convex hull of the chosen points. Which probability is larger: that $C$ is a polygon with three vertices, or a polygon with four vertices?