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#### ATroelstein

##### New member

- Jun 30, 2012

- 15

$(1 - \frac{N}{K}) * (1 - \frac{N}{K - 1}) * (1 - \frac{N}{K - 2}) * ... * (1 - \frac{N}{K - (M-1)})$

I have $K - (M-1)$ as the denominator in the last probability because for the Mth cup, $M - 1$ marbles have been removed from the original set of K marbles. My issue is, in the book I am looking at, it states the probability being

$(1 - \frac{N}{K}) * (1 - \frac{N}{K - 1}) * (1 - \frac{N}{K - 2}) * ... * (1 - \frac{N}{K - M})$

I'm confused as to why their last probability term is $(1 - \frac{N}{K - M})$ as to me it seems like this would be correct if we have $M + 1$ cups. Is there something that I'm missing about how this probability should be calculated? Thanks.