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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-2/27g/a/solution

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Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 2 / 27G / a / Solution by

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

The Borel-Cantelli lemmas are:

If $\sum_{n} P (A_{n}) < \infty$ , then
$P (A_{n} infinitely often) = 0$ .
If the $A_{n}$ are independent and
$\sum_{n} P (A_{n}) = \infty$ , then
$P (A_{n} infinitely often) = 1$ .

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