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Expected number of draws until the first good element is chosen
Expectation of number of trials before success in an urn problem without replacement

Imagine we have a urn in which there are $b$ balls, of which $a$ are black and $b-a$ are white. Now, we keep drawing balls (without putting back) until we get a black ball, let $X$ be the number of draws. What's the expectation of $X$? And does $X$ has some specific distribution?

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marked as duplicate by Raskolnikov, Henry, Cameron Buie, Did, Marc van Leeuwen Nov 4 '12 at 19:37

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Same as math.stackexchange.com/questions/75968/… –  pedrosorio Nov 4 '12 at 18:42
and this math.stackexchange.com/questions/74210/… –  user17762 Nov 4 '12 at 18:44

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