 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ib/paper-3/8h/solution

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

{1, 2, 3, 6}

and

{4, 5}

; only the latter is closed. Let

h_{i} = P_{i} (T_{2} < \infty)

, with

h_{2} = 1

and

h_{4} = h_{5} = 0

. The first-step equations give

h_{3} = 1/2

h_{6} = (h_{1} + h_{3}) /2

, and

h_{1} = 1/3 + h_{3} /3 + h_{6} /6

, hence

h_{1} = 13/22

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