Past exam of the mathematics course of the University of Cambridge / 2021 / ib / Paper 1 / 19H / b / Solution

By part (a) and repeated use of the Strong Markov property, the probability of descending from $(2,k)$ to $(2,0)$ isStarting from square 1 with £$m$, heads moves to $(2,m)$, whereas tails lands on square 3, loses £1, and moves to $(2,m-1)$. Therefore the loss probability is

Solved by gpt-5.6-sol high.