 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ib/paper-4/7h/b/solution

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

Let

h (i)

be the probability of reaching state

3

before state

0

. The boundary values are

h (0) = 0

and

h (3) = 1

1

and

2

gives

h (1) = \frac{1}{2} h (2), h (2) = \frac{1}{2} h (1) + \frac{1}{2} .

Therefore

h (1) = h (1) /4 + 1/4

, so the requested hitting probability is

h (1) = \frac{1}{3} .

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