🧺 Hypergeometric Distribution Calculator
Calculate probabilities for sampling without replacement from a finite population.
📊 Statistics📐 Formula included🧠 Practice questions✓ Free
Please enter valid values.
Formula and Explanation
Calculate probabilities for sampling without replacement from a finite population.
| Concept | Formula or rule |
|---|---|
| Hypergeometric Distribution Calculator | P(X=k) = C(K,k)C(N−K,n−k) / C(N,n) |
How to Use This Calculator
- Enter the sample, counts, probabilities, or summary statistics requested above.
- Keep paired lists in the same order and separate values with commas.
- Select the correct test direction or sample/population option when available.
- Press Calculate and interpret the result together with the supporting statistics.
Worked Example
Example: A box has 10 defective and 40 good items. Five are sampled without replacement.
✓ Use the hypergeometric model because probabilities change after each draw.
Where This Is Used
School & coursework
Check homework, understand formulas, and verify step-by-step statistics exercises.
Research
Explore estimates, uncertainty, distributions, and relationships before using full statistical software.
Business & data analysis
Summarize variation, compare groups, and communicate data-driven findings clearly.
Common Mistakes to Avoid
⚠️
Using binomial for sampling without replacement
Hypergeometric accounts for the changing composition.
Hypergeometric accounts for the changing composition.
⚠️
Entering impossible combinations
k cannot exceed K or n.
k cannot exceed K or n.
⚠️
Confusing N and n
N is population size; n is sample size.
N is population size; n is sample size.
Practice Questions
1. Which model fits drawing cards without replacement?
Answer: Hypergeometric.
2. If N=100, K=20, n=10, what is the expected number of successes?
Answer: 2
3. Can n exceed N?
Answer: No.
Frequently Asked Questions
When is binomial a reasonable approximation?▾
When the sample is a small fraction of a large population.
What is the mean?▾
nK/N.
Are draws independent?▾
No, not when sampling without replacement.