Exam mode different distribution (Difficulty: Medium)

Question: In a forum an important question is asked. Persons who formulate an answer give the correct answer with a 71% probability. How many people have to answer at least to the question, so you at least get a correct answer with a probability of at least 92%?

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Binomial

Formula:

Binomialverteilung Formel

Properties of the Binomial

Expected value μ = E(X) = n*p

Variance σ² = Var(X) = n*p*q = n*p*(1-p)


Hypergeometric distribution

Formula:

Hypergeometrische Verteilung Formel

Properties of the Hypergeometric distribution

Expected value μ = E(X) = Hypergeometrische Verteilung Erwartungswert Formel

Variance σ² = Var(X) = Hypergeometrische Verteilung Varianz Formel


Inclusion-exclusion principle

Two quantities
|A ∪ B| = |A| + |B| - |A ∩ B|

Three quantities
|A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|