Past exam of the year 1 of the computer science course of the University of Oxford / 2017 / Discrete mathematics, continuous mathematics and probability / 8 / b / i

Starting at $X$, the two possible two-step returns are $X\to X\to X$ and $X\to Y\to X$. They are disjoint events, with probabilities $1/4$ and $3/16$. ThereforeEach path probability uses the specified Markov property to multiply its successive transition probabilities.