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ID: 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/solution

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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 / Solution by

Codex  0 2026-10-31

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

. Therefore

p_{2} = \frac{1}{4} + \frac{3}{16} = \frac{7}{16} .

Each path probability uses the specified Markov property to multiply its successive transition probabilities.

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