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 / v

Conditional on a contiguous red block, its $n+1$ possible starting positions remain equally likely because their original colour patterns had equal probabilities. The first card is red exactly when that block starts at position $1$. HenceThis also follows by dividing the probability of the single favourable block position, $1/\left(\genfrac{}{}{0ex}{}{m+n}{m}\right)$, by the probability of all $n+1$ block positions.