Geometric Distribution Calculator
Find the chance that the first independent success occurs on a chosen trial.
Result for the values shown.
Calculations run in your browser.
What to enter
| Input | Meaning and units |
|---|---|
| Success probability | decimal(0,1] |
| Successes / event count | integer>=1 |
Understanding your result
These outputs describe the probability model and event definitions you entered. A probability is a number from 0 to 1; a probability density is not itself the probability of one exact continuous value.
Common mistakes
- Entering 25 instead of 0.25 for a probability, or assuming events are independent when the model requires that assumption.
- Confusing an exact-count probability with a cumulative probability, or replacement with sampling without replacement.
Check your calculation
- Check a zero/certain-event boundary and the stated support of the distribution against the worked example.
Calculation checks, sources and review limits
What is the chance that the first independent success happens on this trial?
Find the chance that the first independent success occurs on a chosen trial.
Common uses
- Find the chance that the first independent success occurs on a chosen trial.
How it works
P(K=k)=(1-p)^(k-1)*p, K=trial index of first success. Trials/draws/counts are limited to 10,000; negative-binomial r and k may each be at most 10,000. Log-factorial arithmetic avoids forming large factorials. Extremely small probabilities can underflow to zero; outputs are numerical estimates, not guarantees about real events.
Worked example
Enter Success probability: 0.5; Successes / event count: 3. The result is Pmf: 0.125.
FAQ
What is the chance that the first independent success happens on this trial?
P(K=k)=(1-p)^(k-1)*p, K=trial index of first success. Trials/draws/counts are limited to 10,000; negative-binomial r and k may each be at most 10,000. Log-factorial arithmetic avoids forming large factorials. Extremely small probabilities can underflow to zero; outputs are numerical estimates, not guarantees about real events.
What assumptions and limits apply?
Counts trials including success; not number of failures.