A probability problem.

Forum for the GRE subject test in mathematics.
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A probability problem.

Post by conrado.math » Wed Sep 30, 2009 7:41 pm

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...

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Re: A probability problem.

Post by diogenes » Sat Oct 24, 2009 4:49 am

hmmm...tricky problem.

Any hints :wink:

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