Geometric Distribution Calculator
Find the probability that the first success in a series of independent trials happens on a specific attempt.
What the geometric distribution models
The geometric distribution gives the probability that the first success in a sequence of independent trials, each with the same success probability p, occurs on a specific trial number k. It is commonly used to model things like the number of attempts until a first sale, a first defect, or a first heads on a coin flip.
How this calculator works
Enter the probability of success on each individual trial and the trial number you are interested in. The calculator finds the probability mass function P(X = k) = (1 – p)k-1 × p, the probability the first success happens by or before trial k, and the expected (average) number of trials needed for a first success, which is 1/p.
This calculation assumes every trial is independent and has the same fixed probability of success. It is intended for general statistics education and planning use.