## A probability problem.

Forum for the GRE subject test in mathematics.
conrado.math
Posts: 9
Joined: Tue Sep 29, 2009 1:07 pm

### A probability problem.

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
Posts: 73
Joined: Sun Aug 31, 2008 9:31 pm

### Re: A probability problem.

hmmm...tricky problem.

Any hints

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