Calculate waiting-time probabilities for the first success in repeated trials.
Last updated: June 2026 | By Patchworkr Team
The geometric distribution describes the number of trials needed until the first success.
Geometric distribution measures how long it takes to see the first success.
P(X = k) = (1 - p)^(k - 1) x p and E[X] = 1 / p.
First six on a fair die.
p = 1/6
k = 4
P(X = 4) = (5/6)^3 x (1/6)
About 0.0965
How is this different from binomial distribution?
Binomial counts successes in a fixed number of trials. Geometric counts trials until the first success.
Why is the probability type selectable?
It lets you view the exact first-success probability, cumulative probability, or survival probability.
Can p equal 1?
Yes. In that case the first trial succeeds with probability 1 and the median is 1.
What if k is less than 1?
That is invalid because the first trial number must be at least 1.
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