TITLE: Geometric Without Replacement?
QUESTION [7 upvotes]: Is there a probability distribution corresponding to a geometric distribution without replacement? By this I mean the idea of the time until the first success, but with dependent rather than independent events?
For example, the time it takes until you draw a spade from a standard deck of $52$ cards? Or if you have $5$ red and $5$ blue marbles in an urn, the time it takes until you draw a blue marble?
Is this just the hypergeometric distribution? I am inclined to say no because the hypergeometric distribution specifies the number of samples.

REPLY [6 votes]: Yes, I believe it's called the negative hypergeometric distribution.
Here is a pdf on the matter. I quote the following:

The Negative Hypergeometric Distribution
Let $Y$ be a random variable counting the number of selections required required until the $k$th success is obtained when sampling without replacement from a set of $N$ objects of which $M$ have a certain attribute (i.e. success). then $Y$ is said to have a Negative Hypergeometric distribution with parameters $N$, $M$, and $k$ -- that is, $Y\sim\operatorname{NHG}(N,M,k)$ -- and, for appropriate values $y$, its probability function is 
  $$p_Y(y)\equiv P[Y=y] = \frac{\binom{M}{k-1}\binom{N-M}{y-k}}{\binom{N}{y-1}}\times \frac{M-k+1}{N-y+1}.$$