# Expected value

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#14. An urn has m black balls. At each stage a black ball is removed and a new ball, that is black with probability p and white with probability 1 - p, is put in its place. Find the expected number of stages needed until there are no more black balls in the urn.

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This shows how to find the expected number of stages needed until there are no more black balls in the urn.

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When 1 ball is taken out, there will be m black balls left. And the put-in ball is black with probability p

Then the expected number of black balls after ...

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