Statistics & Probability

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Hypergeometric Distribution Calculator.

Calculate this statistic instantly with validated formulas.

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Results update as you type.

Result: P(X=2): 0.3873839009

Result

P(X=2): 0.3873839009

Use Cases

Quality Control Sampling

Determine the probability of finding a certain number of defective items in a sample drawn from a batch, without replacement.

Example: If a batch of 100 items has 10 defects, what's the chance a sample of 20 contains exactly 2 defects?

Card Game Probabilities

Calculate the likelihood of drawing a specific number of aces or cards of a suit from a deck without replacement.

Example: In a 5-card hand from a standard deck, what's the probability of getting exactly 2 hearts?

Frequently Asked Questions

What is the hypergeometric distribution?
The hypergeometric distribution models the probability of drawing a specific number of successes from a finite population without replacement. It's used when each draw changes the composition of the population, unlike the binomial distribution which assumes replacement.
How do I use this calculator?
Enter the population size, number of successes in the population, sample size, and the number of successes you want to observe in the sample. The calculator will compute the probability of getting exactly that many successes, as well as cumulative probabilities.
What are the inputs required?
You need four values: population size (N), number of successes in the population (K), sample size (n), and the number of successes in the sample (k). All must be non-negative integers with k ≤ n and K ≤ N.

Tips & Common Mistakes

Tips

  • Ensure all inputs are non-negative integers; the calculator expects whole numbers.
  • The number of successes in the sample (k) cannot exceed the sample size (n) or the total successes in the population (K).
  • Use cumulative probabilities to find the chance of getting at least or at most a certain number of successes.
  • Double-check that your population size is the total number of items, not just the ones you're sampling from.

Common Mistakes to Avoid

  • Confusing hypergeometric with binomial: hypergeometric is without replacement, so probabilities change after each draw.
  • Entering values in the wrong order: population size, successes, sample size, and observed successes must match the calculator's fields.
  • Using percentages instead of counts: inputs must be actual counts, not percentages or proportions.

Last updated: August 13, 2026