Suppose there are $m$ red balls and $n$ blue balls in an urn. We randomly choose $p:m<p<n$ balls uniformly from the urn. What is the probability that exactly $q$ red balls are chosen?
Note:- Normally the answer would be $\frac{{m}\choose{q}}{{m+n}\choose{q}}$. However, since the number of balls that are chosen are provided, it is confusing me out. Any hints for the answer will also be appreciated.
Best Answer
What you describe is a Hypergeometric Distribution of sampling without replacement.
It follows that
$$P(X=q)=\frac{{{m}\choose{q}}{{n}\choose{p-q}}}{{{m+n}\choose{p}}}$$