 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ib/paper-4/7h/b/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

On the closed class, the transition matrix is

(1/3 1/4 2/3 3/4) .

(3/11, 8/11)

. The class is irreducible and aperiodic because of its self-loops, while the other class is transient and enters it almost surely. Hence

lim_{n \to \infty} P^{n} = 0000 3/11 3/11 3/11 3/11 0000 8/11 8/11 8/11 8/11 .

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