Past exam of the year 1 of the computer science course of the University of Oxford / 2021 / Discrete mathematics, continuous mathematics, and probability / 8 / a / i

Let $N=m+n$. In a uniformly shuffled deck, each labelled card is equally likely to occupy the first position, and exactly $m$ cards are red. Therefore $\mathbb{P}(\text{first red})=m/(m+n)$. Equivalently, the red positions are a uniformly chosen $m$-element subset of the $N$ positions.