Question 77
For $i = 0, 1, \ldots, 5$ let $l_{i}$ be the ray on the Cartesian plane starting at the origin, at angle $\theta = i \frac{\pi}{3}$ counterclockwise from the positive $x$-axis. For each $i$, point $P_{i}$ is chosen uniformly at random from the intersection of $l_{i}$ with the unit disk. Consider the convex hull of the points $P_{i}$, which will (with probability 1) be a convex polygon with $n$ vertices for some $n$. What is the expected value of $n$?