Geometric distribution calculator
The model counts independent trials until the first success, so X starts at 1.
Probabilities around the selected k
| k | P(X = k) | P(X ≤ k) | P(X ≥ k) |
|---|---|---|---|
| Fill in the fields above — the result is computed on this page. | |||
How to use this page
- Choose a probability calculation or quantile.
- Enter p and k or quantile level q.
- Compare the result with the mean and nearby k values.
What this page does not do: The model requires constant p and independent trials. Do not use it when probability changes over time or when sampling without replacement from a small population.
Further reading
The geometric distribution gives the trial number on which the first success occurs when every trial has the same probability p and trials are independent. Under this convention X can be 1, 2, 3 and so on.
Its memoryless property means that after a run of failures the chance of success on the next trial is still p. Past outcomes do not raise the probability of the next independent trial.
Frequently asked questions
Does X count failures or all trials?
This page defines X as all trials up to and including the first success, so the smallest X is 1.
Does success become more likely after many failures?
Not in this model. With independent trials the probability on every next trial remains p.
See also
Beta distribution calculator
Calculate beta density, CDF, upper tail and quantile together with its mean and variance.
Chi-square test calculator
Calculate chi-square goodness of fit, independence, or a chi-square critical value.
Continuous uniform distribution calculator
Calculate density, CDF, upper tail, quantile, mean and variance for U(a,b).