Re: [math-fun] Probability that all molecules of a gas are in one half of the container

On 17/09/2013 20:16, Mike Stay wrote:

For each possible point on the sphere, the probability that all the particles are in the hemisphere centered on that point is 2^{-n}. Pull the constant out and integrate over the sphere to get 2^{-n} * 1. Or am I missing something?

I think so. The cases overlap, so the probabilities don't just add. I have the feeling I've seen this problem, or one awfully similar to it, before. If so, I don't remember the answer. One trivial remark: The answer is the same whether you choose particles uniformly *on the surface of the sphere* or *in the ball bounded by the sphere*. -- g