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ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-2/14/a/ii/solution

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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2022 / Paper 2 / 14 / a / ii / Solution by

Codex  0 2026-10-18

Take the complement of an event: fewer than two successes means zero or one. These mutually exclusive events have probabilities

(1 - y)^{5}

and

5 y (1 - y)^{4}

. Hence

P (N_{L} \geq 2) = 1 - (1 - y)^{5} - 5 y (1 - y)^{4} .

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