 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-1/27l/a/solution

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

P (⋃_{n \geq m} A_{n}) \leq \sum_{n \geq m} P (A_{n}) \to 0

. For independent events in the divergent case,

P (none of A_{m}, \dots, A_{n}) = \prod_{j = m}^{n} (1 - p_{j}) \leq e^{- \sum_{j = m}^{n} p_{j}} \to 0,

and then let

m \to \infty

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