What Is the Hypergeometric Distribution Calculator?
A hypergeometric distribution calculator determines combinatorial probabilities for finite finite-population sampling without replacement.
How Does the Hypergeometric Distribution Calculator Work?
Evaluates binomial coefficients across favorable and non-favorable subsets relative to total sample combinations.
Hypergeometric Distribution Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
P(X = k) = [C(K, k) × C(N - K, n - k)] ÷ C(N, n)
Multiplies combination of choosing k successes from K by combination of choosing remaining failures, divided by total sample combinations.
How to Use the Hypergeometric Distribution Calculator
- Input population size N, total population successes K, sample draws n, and desired sample successes k.
Step-by-Step Example Calculation
Drawing 2 Aces in 5 Cards from a 52-card Deck
Input Values:
popN:52
popSuccessesK:4
sampleN:5
sampleSuccessesk:2
Understanding Your Result
Outputs exact probability of observing precisely k successes and expected mean successes in the draw.
Factors That Affect the Result
- Population size and sample proportion.
When Should You Use This Calculator?
- Card gaming odds, lotteries, manufacturing acceptance sampling without replacement, and wildlife capture-recapture studies.
Assumptions & Limitations
- Items cannot be sampled more than once in a single trial.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Exact combinatorial formulation.