How to use the hypergeometric probability calculator
Find the probability of drawing k successes without replacement. Enter population size, successes in population, draws, successes drawn in the fields above; the p(x = k) is computed instantly and plotted on the chart so you can see how the answer changes.
Common searches this calculator answers include “drawing cards”, “lottery”, “sampling without replacement”, “calculate hypergeometric probability”, “find p”.
Formula
Variables
- N — Population size
- K — Successes in population
- n — Draws
- k — Successes drawn
Worked example
With population size = 52, successes in population = 13, draws = 5, successes drawn = 2, the calculator gives p(x = k) ≈ 0.2742797.
Frequently asked questions
What is the hypergeometric probability calculator used for?
Find the probability of drawing k successes without replacement. It helps with questions such as “drawing cards”, “lottery”, “sampling without replacement”.
What is the formula for the hypergeometric probability calculation?
P(X = k) = nCr(K,k) × nCr(N-K,n-k) / nCr(N,n). Here N is population size, K is successes in population, n is draws, k is successes drawn.
What inputs do I need for the hypergeometric probability calculator?
You need population size, successes in population, draws, successes drawn. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use the hypergeometric probability calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the hypergeometric probability result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.