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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/2019/paper-2/6/a/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 / 2019 / Paper 2 / 6 / a / Solution by

Codex  0 2026-10-18

The inclusion-exclusion principle for probabilities gives

P (A \cup B \cup C) = P (A) + P (B) + P (C) - P (A \cap B) - P (A \cap C) - P (B \cap C) + P (A \cap B \cap C) .

(1)

Each outcome belonging to two events is initially counted twice and must lose one count. An outcome in all three is counted three times and then subtracted three times, so the last term restores its single count.

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