Probability distribution for sampling without replacement from a finite population.
Population Parameters
Sample Parameters
Formula Definition
P(X=k) = [C(K,k) * C(N-K, n-k)] / C(N,n)
Probability Analysis
Exact Probability P(X = k)27.428%Exact probability for specified k
P(X ≤ k)90.72%
P(X ≥ k)36.70%
Expected Mean (μ)
1.250
Std Deviation (σ)
0.930
Sampling without replacement: probability changes with each draw.
About this calculator
Overview
The Hypergeometric Distribution is used for sampling without replacement from a finite population. Unlike the Binomial distribution, where the probability of success remains constant, here the probability changes with every draw because the population size and composition decrease.
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Pro Tips
All parameters (N, K, n, k) must be non-negative integers.
Sample size n cannot exceed population size N.
Desired successes k cannot exceed population successes K or sample size n.
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Fun Facts
"Commonly used to calculate card game odds, like the chance of drawing a specific suit in poker."
"Used in quality control tests where products are destroyed during testing (destructive sampling)."
"As the population size N becomes very large relative to the sample size n, it converges to the Binomial Distribution."
