A probability problem.

[conrado.math]

I saw yesterday in this forum a discussion on a problem that asked to determine what's the probability of choosing three points $$x,y,z\in[0,1]$$ such that $$yz\leq x$$. The answer is $$\frac{3}{4}$$ 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.

Problem: What is the probability of choosing four points on the unit sphere $$\mathbb S^2$$ 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...

[diogenes]

hmmm...tricky problem.

Any hints