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?

Proposed by Fedor Petrov, St. Petersburg State University