HMMT 2025 U9

Let $P$ and $Q$ be points selected uniformly and independently at random inside a regular hexagon $ABCDEF$ . Compute the probability that segment $\overline{PQ}$ is entirely contained in at least one of the quadrilaterals $ABCD$ , $BCDE$ , $CDEF$ , $DEFA$ , $EFAB$ , or $FABC$ .