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 December 30th, 2010, 08:30 AM #1 Newbie   Joined: Dec 2010 Posts: 2 Thanks: 0 Probability of seeing k different colors in sample of size m Hi all, it would be great if anyone could help me with a particular problem: Imagine an urn with a certain number marbles of different colors. It is known how many marbles of certain color are contained. The question is: If we draw m times from the urn (with placing back), how likely is it, to see k different colors in the sample? And: Which number of different colors is most likely to be observed? I think that the answer to this is not trivial, or at least not easy to compute analytically, and I would be very happy to be proven wrong. Thanks for any help on this, duffy
 December 30th, 2010, 09:39 AM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Probability of seeing k different colors in sample of si
 December 30th, 2010, 03:37 PM #3 Newbie   Joined: Dec 2010 Posts: 2 Thanks: 0 Re: Probability of seeing k different colors in sample of si Thanks for the link, CRGreathouse. The question answered there is certainly somehow related to mine, but different. They asked how many unique marbles are found in the sample. My question was how many different types of marbles are found in the sample.
December 30th, 2010, 09:40 PM   #4
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Re: Probability of seeing k different colors in sample of si

Quote:
 Originally Posted by duffy Thanks for the link, CRGreathouse. The question answered there is certainly somehow related to mine, but different. They asked how many unique marbles are found in the sample. My question was how many different types of marbles are found in the sample.
It's the same question. Suppose you have 3 red marbles out of 100 in total. To convert that to the other form, treat it as a single marble that is drawn with probability 0.03.

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