Consider drawing $n$ balls from an urn containing $N$ balls, of which $m$ are red. If i know $N$, $m$ and $n$ i can use the hypergeometric distribution to calculate the probability that my sample contains exactly $k$ red balls, and using the cumulative distribution i can get the probability to get at most $k$ red balls.
Can i calculate the probability that a total $m$ of all balls are red if i know the number of reds $k$ in my sample? I'm mainly interested in bounding $m$:
$\Pr(m>m_{max}|k=k_{sample})<\epsilon$
My first idea was to use the hypergeometric distribution with $m$ as random variable and norm it so the sum over all $m$ is 1. Is that a valid approach to calculate probabilites and bounds on $m$?
