Am Wed, 17 Dec 2008 14:49:38 +0100 schrieb scott:

> If you have a box with N balls numbered 1 to N, and you repeatedly pull
> one out at random (replacing it each time), on average how many times
> would you expect to pull out a ball until you have seen all the balls 1
> to N?

Without looking at the other solutions (and excluding the trivial case), 
I would guess, that such average number does not exist. There is the real 
possibility of always pulling the same ball. In fact there is an infinite 
number of such combinations, where you can pull balls without ever 
getting all the balls. If the pulling of balls is truely random and 
independently, such combinations are not less likely (seems unintuitive, 
but there is no way of predicting which ball you will pull based on which 
balls you already pulled). In this case the infinite sum is diverging and 
you can't calculate an average.

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