Arcs of length lk, 0 < lk < 1, k = 1, 2, ···, n, are thrown independently and uniformly on a circumference
having unit length. Let P(l 1 , l 2, · ··, ln ) be the probability that
is completely covered by the n random arcs. We show that P(l 1 , l 2 ,· ··, ln ) is a Schur-convex function and that it is convex in each argument when the others are held fixed.