What this calculator does
Negative binomial probability works out chance that the rth success happens on exactly the kth independent trial. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
FormulaP(X=k) = C(k−1, r−1)·pʳ·(1−p)ᵏ⁻ʳ; mean = r/p, variance = r(1−p)/p²
The inputs explained
| Field | What to enter |
|---|---|
| Successes needed (r) | A number. Starts at 3. |
| Success probability per trial (%) | A number, measured in %. Starts at 40. |
| Trial of the rth success (k) | A number. Starts at 8. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with successes needed (r)
Every other input is held at the calculator’s starting values while successes needed (r) varies. Select any row to load that scenario into the calculator.