Urn Problem

Problem

• We have $N$ balls in total
• $m$ balls are white
• $N-m$ balls are black
• We pick $n$ balls without replacement

Proposed Solution

A Hypergeometric Distribution with RV $X$ to denote the # of white balls out of $n$ balls chosen.

Example

• With $N=10$
• With $m=7$
• With $N-m=3$
• With $n=5$ Then,
• $x=2,3,4,5$
• In general, $P(X=x)=\frac{\left(\genfrac{}{}{0ex}{}{m}{x}\right)\left(\genfrac{}{}{0ex}{}{N-m}{n-x}\right)}{\left(\genfrac{}{}{0ex}{}{N}{n}\right)}$