Hypergeometric Calculator
Calculate the probability of k successes in n draws without replacement from a finite population of size N containing K successes.
Published by:
isCalculator Editorial Team
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How to use this tool?
This calculator computes the probability of exactly k successes in n draws without replacement from a finite population.
Step-by-Step Instructions
- Enter Population Size (N): The total number of items in the population (e.g., 50). Must be a positive integer.
- Enter Number of Successes in Population (K): How many of those items are considered "successes" (e.g., 10). Must be between 0 and N.
- Enter Sample Size (n): How many items you draw without replacement (e.g., 5). Must be between 0 and N.
- Enter Number of Successes in Sample (k): The exact number of successes you want the probability for (e.g., 2). Must be between 0 and n, and cannot exceed K.
- Click "Calculate Probability": The result shows the probability (as a decimal) and the formula used.
Important Notes
- All inputs must be non-negative integers (whole numbers).
- Population size (N) must be at least 1.
- The calculator validates that K ≤ N, n ≤ N, k ≤ n, and k ≤ K.
- The result is displayed with 6 decimal places.
Previous Results
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Frequently Asked Questions
The hypergeometric distribution models the probability of obtaining exactly k successes in n draws without replacement from a finite population of size N that contains exactly K successes.
Enter the population size (N), number of successes in population (K), sample size (n), and number of successes in sample (k). Then click 'Calculate Probability' to get the probability.
All inputs must be non-negative integers. K must be ≤ N, n must be ≤ N, and k must be ≤ n and ≤ K. The calculator will show an error if constraints are violated.
