Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2007 / Paper 2 / Section A / 9

There are $\left(\genfrac{}{}{0ex}{}{7}{2}\right)=21$ equally likely unordered pairs, and $3\cdot 4=12$ contain one ball of each colour. Thus the hypergeometric distribution gives

Let $I_1,I_2$ be indicator random variables for the two draws being red. Each draw has red probability $3/7$, even though the draws are dependent. By linearity of expectation, the number $R=I_1+I_2$ satisfies