Exam mode different distribution (Difficulty: Easy)

Question: The probability that a bee colony survives an intense winter is 90%. A beekeeper owns 8 colonies. What is the probability that at least 6 colonies survive an intense winter?

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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|