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An urn contains $n$ balls, all different colors. A person draws a ball randomly, records the color before replacing it. The person must record all colors in order to receive a large prize. If $m$ colors have been recorded so far, what is the probability that it will take exactly $x$ draws to get a new color?

By Bernoulli trial, the probability of a success would be : $(N-M)/M$. Probability of a failure is $M/N$. now the probability that it will take $x$ trials to get a success would be, =>

$$\frac{N-M}{M} \left(\frac{M}{N}\right)^{1-X}$$ => am i correct?

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    What do $N$, $M$ stand for and what is the relationship between them and $n$, $m$?2011-11-23
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    This is related to a well-known problem called the Coupon Collector problem. Have you looked that up?2011-11-23
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    Please unifiy uppercase and lowercase letters. Also, check the denominator in your probability of a success expression.2011-11-23
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    @DimitrijeKostic: " The person must record all colors in order to receive a large prize. " sounds as the Coupon Collector problem. But the real question (what follows) is not.2011-11-23
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    @leonbloy I can see that the question being asked isn't precisely the Coupon Collector problem. The question contained no reference to "the Coupon Collector" problem so I said, correctly, that this question is "related."2011-11-23
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    This is a repeat post: http://math.stackexchange.com/questions/84864/probability-urn-question2011-11-23

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