Suppose you realize $n$ draws—with no replacement—from a sample of $N$ marbles, in which I know there are $K$ white marbles and $N - K$ black marbles. The probability of getting $k \leq n$ white marbles is given by a hypergeometric distribution.
Now imagine $n$ is quite big and $N$ is even bigger, and what you are interested in is no the number of successes $k$, but the ratio of white to black marbles you end up drawing, $P = k/n$. I assume $n$ is large enough that $P$ is practically a continous variable with support on $[0, 1]$. Is there a distribution function I could use to find the probability that $P \leq p$, for $0 \leq p \leq 1$?
Thanks for your help.
