I saw yesterday in this forum a discussion on a problem that asked to determine what's the probability of choosing three points
. The answer is
and there is a number of ways of finding it. I'd like to propose another problem similar to this. It's from Shiryaev's classic book Probability
What is the probability of choosing four points on the unit sphere
such that the center of the sphere is contained in the region delimited by the (not necessarily regular) tetrahedron whose vertices are these four points?
I believe anyone who solves this problem will find the one mentioned above quite trivial...