Calculate Probabilities and Statistics with Step-by-Step Derivation
Population Size (N)
Population Successes (K)
Sample Size (n)
Number of Successes (k)
Results
P(X=k)
P(X≤k)
P(X≥k)
Mean (μ)
Variance (σ²)
Std Dev (σ)
Step-by-Step Derivation
Hypergeometric Distribution Formulas
P(X=k) = [C(K,k) × C(N-K, n-k)] / C(N,n)
Mean μ = n × K / N
Variance σ² = n × (K/N) × ((N-K)/N) × ((N-n)/(N-1))
Where C(a,b) is the combination of a items taken b at a time!
⚠Hypergeometric distribution is for sampling without replacement from finite populations.
What is Hypergeometric Distribution?
Hypergeometric distribution models the probability of k successes in n draws without replacement from a finite population of size N containing K successes.
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