Let n,k≥3 be integers, and let S be a circle. Let n blue points and k red points be
chosen uniformly and independently at random on the circle S. Denote by F the intersection of the
convex hull of the red points and the convex hull of the blue points. Let m be the number of vertices
of the convex polygon F (in particular, m=0 when F is empty). Find the expected value of m.
probability and statsexpected valuecombinatoricscombinatorial geometryIMC 2022