CMIMC 2020 Geometry Problem 11

(Estimation) Gunmay picks 6 points uniformly at random in the unit square. If p is the probability that their convex hull is a hexagon, estimate p in the form 0.abcdef where a, b, c, d, e, f are decimal digits. (A convex combination of points x_{1}, x_{2}, \ldots, x_{n} is a point of the form \alpha_{1} x_{1}+\alpha_{2} x_{2}+\cdots+\alpha_{n} x_{n} with 0 \leq \alpha_{i} \leq 1 for all i and \alpha_{1}+\alpha_{2}+\cdots+\alpha_{n}=1. The convex hull of a set of points X is the set of all possible convex combinations of all subsets of X.)