Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2015 / Paper 1 / 16 / a / v

Let $I_j$ be the indicator random variable of a black ball at draw $j$. The black count after three draws is $N(B_3)=I_1+I_2+I_3$. By linearity of expectation,Independence is not required for this step. This is also the mean of the corresponding hypergeometric distribution.