Past exam of the mathematics course of the University of Cambridge / 2024 / ib / Paper 4 / 7H / b / ii / Solution

Let $p_n=\mathbb{P}(X_n=A)$. Whenever the taxi is away from the airport it returns with probability $3/4$, whereas it must leave whenever it is at the airport. HenceSubtracting the fixed point $3/7$ givesThereforefor every $n\ge 0$, and in particular for the requested $n\ge 1$.

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