 Solution

ID: 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/solution

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 $P (first red) = m / (m + n)$ . Equivalently, the red positions are a uniformly chosen

m

-element subset of the

N

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