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August 25th, 2013, 01:00 AM   #1
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Probabily & Expectedvalue of samples from a large distributi

The practical application of this problem is a collectable card game

lets say they print X cards, where X is unknown (though we could make assumptions). There are 101 individual cards that each occur equally frequently within the total print run, but we do not know if the print run is 5 copies of each card, 1000 copies, or a million.

If I buy a booster box that has 360 cards randomly taken from this global collection


is there an expression that calculates the probability I get each unique type within that 360
is there an expression that calculates the expected number of unique types in my set of 360

or is it impossible without specifically stating the total size of the worldwide collection?

thanks in advance
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August 25th, 2013, 12:36 PM   #2
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Re: Probabily & Expectedvalue of samples from a large distri

This will depend on the number of each card. If only 5 of each, there is a total of 505 printed, so when dealing with 360 you need to take into account that the maximum is 5 for any card. When the total printed is very much larger (say 1000 per card) then you can neglect this issue (although it has some minimal effect).
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