Past exam of the mathematics course of the University of Cambridge / 2024 / ia / Paper 2 / 10F / ii / Solution

When exactly $n-j$ faces have appeared, there are $j$ unseen faces, so each new roll discovers one with probability $j/n$. Let $G_j$ be the number of further rolls needed at that stage. ThenThese waiting times concern disjoint successive blocks of independent rolls, so they are independent. Thus the coupon collector problem has the decomposition