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Q91 / 100
What is the Bonferroni inequalities and their use in probability?
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The correct answer is B) Alternating inequalities bounding P(A₁∪...∪Aₙ) from above and below using sums of k-wise intersection probabilities — used to compute probability of at least one event
B
Correct Answer
Alternating inequalities bounding P(A₁∪...∪Aₙ) from above and below using sums of k-wise intersection probabilities — used to compute probability of at least one event
Explanation
Inclusion-exclusion alternates: P(∪) ≤ Σ P(Aᵢ) (union bound), P(∪) ≥ Σ P(Aᵢ) - Σ P(Aᵢ∩Aⱼ), etc. Odd sums upper bound, even sums lower bound. Used in derangements, hat-check problems, and prime sieve analysis.
Progress
91/100