Calculate successes in a sample drawn without replacement. Beside sample probability, the output shows the operation used to obtain it.
From N=50 with K=12, drawing 8 and observing 3 successes has probability about .2057.
Hypergeometric probability C(K,k)C(N−K,n−k)/C(N,n) counts successes in a sample drawn without replacement.
For a Hypergeometric Distribution audit, retain Population size N and Population successes K. Decide the likely direction of Sample probability before rerunning Hypergeometric Distribution. Change only Draw count n; the response in Sample probability can then be traced within the Hypergeometric Distribution setup.
All counts must be mutually possible. Unlike binomial trials, draws are dependent because objects are not returned.
Choose requested successes and failures separately, then divide by every sample of size n. Hypergeometric Distribution also leads to replacement comparison.
Link Population size N to its Hypergeometric Distribution role. Link Population successes K to its Hypergeometric Distribution role. The retained Hypergeometric Distribution formula identifies the Hypergeometric Distribution model.
It fits card hands, lot inspection, roster samples, and finite inventories. A related application of Hypergeometric Distribution is sample counts.
Exact arrangement counts from Hypergeometric Distribution should not be shortened to a decimal approximation. Probability calculations based on Population size N, Population successes K, Draw count n, Sample successes k may be rounded for presentation, but their intermediate products and cumulative sums need extra digits so the final tail or complement is not distorted.
Classify Population size N before using Hypergeometric Distribution. Confirm that Population successes K fits the allowable Hypergeometric Distribution range.
Test a zero or certain-event Hypergeometric Distribution boundary. Compare that simple Hypergeometric Distribution case with Population successes K.
Before using Sample probability downstream, substitute a simple Population size N into the same Hypergeometric Distribution relation. Preserve Population successes K so the comparison remains fair. The resulting Sample probability provides a benchmark for detecting a misplaced sign, decimal, or input order.
No.
When the sampling fraction is small.
No.
It counts all equal-size samples.