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Past exam of the mathematics course of the University of Cambridge / 2025 / ia / Paper 2 / 9F / c / Solution

With

p = (1 + ε) lo g n / (n - 1)

, the union bound gives

P (L = 0) \leq n (1 - p)^{n - 1} \leq n e^{- p (n - 1)} = n^{- ε} .

Solved by gpt-5.6-sol high.

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