The hypergeometric distribution models a fixed-size draw without replacement.
Hypergeometric Calculator
Form
Results
Chance to draw 4 or more of the wanted card
0
Chance to draw exactly 4 of the wanted card
0
Chance to draw 4 or less of the wanted card
0
Chance to draw 0 of the wanted card
0
Table of Contents
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What is Hypergeometric?
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How to Use This Calculator
- Enter or select Population Size (N), Sample Size (n), Successes in population (K), Successes in Sample (k).
- Check the unit beside each measurement. For a percentage or rate, use the scale and time period stated in the form.
- Choose Calculate, then compare the output with the formula and example below. If you change a value or option, calculate again to update the result.
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Formula Used
P(X=k)=C(K,k)C(N−K,n−k)/C(N,n)
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Variables Explained
| Input | What it means |
|---|---|
| Population Size (N) | Total number of eligible members in the population being studied. |
| Sample Size (n) | Number of observations or responses in the sample, rather than the population size. |
| Successes in population (K) | Total number of eligible members in the population being studied. |
| Successes in Sample (k) | Use the measured or stated value for this item, with the unit or category shown beside the field. |
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Worked Example
From 10 objects with 4 successes, drawing 2 gives P(both successes)=6/45≈0.1333.
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Why Use This Calculator?
Calculate draw probabilities when selections are made without replacement.
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Common Mistakes
- Sampling without replacement makes draws dependent; do not substitute a binomial model without checking.
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Frequently Asked Questions
Does a calculated statistic prove a conclusion?
A statistic describes the supplied data under stated assumptions. Sampling design, missing observations and the suitability of the model still determine what can reasonably be concluded.
Should I include every observation?
Use the observations required by your study design and state any exclusion rule. Removing values only because they change the answer can bias the analysis.
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Sources & References
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