Negative Binomial Probability
Negative Binomial Probability with explicit assumptions and reproducible inputs.
Formula
- Use the units shown beside each field.
- Results update automatically whenever you change an input.
- Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
- Independent Bernoulli trials with constant p. K counts failures, not total trials. Numerical results are approximate. Extremely small probabilities can underflow to zero. No personal, clinical or financial decision rule is inferred.
Example Calculation
- Required successes r: 3
- Failures before rth success k: 2
- Success probability p: 0.5
Before the third success, exactly two failures at p0.5 have probability 6/32=0.1875.
Frequently asked questions
How do I use this calculator?
Enter required successes r, failures before rth success k, success probability p. The result updates automatically. Use Reset to restore the example values.
What method does it use?
P(K=k)=C(k+r−1,k)pʳ(1−p)ᵏ. Independent Bernoulli trials with constant p. K counts failures, not total trials. Numerical results are approximate. Extremely small probabilities can underflow to zero. No personal, clinical or financial decision rule is inferred.
Why might a rounded result differ?
The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.
Are my inputs saved online?
No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.
Check the assumptions and units before using this result. Read about calculation methods.