Question 50
Po picks 100 points $P_{1}, P_{2}, \ldots, P_{100}$ on a circle independently and uniformly at random. He then draws the line segments connecting $P_{1} P_{2}, P_{2} P_{3}, \ldots, P_{100} P_{1}$. When all of the line segments are drawn, the circle is divided into a number of regions. Find the expected number of regions that have all sides bounded by straight lines.