Geometric Distribution Calculator
Find the probability that the first success occurs on a specific trial.
Geometric Distribution Formula
P(X = k) = (1 − p)k−1p, where p is the probability of success on each independent trial.
This model is useful when counting how many trials are needed before the first success.
How the Geometric Distribution Works
The geometric distribution models the number of trials needed to obtain the first success when each trial has the same success probability and trials are independent.
Geometric Example
If the probability of success on each trial is 0.25, the calculator can estimate the probability that the first success occurs on a specific trial.
When It Fits
This model is appropriate for repeated yes/no trials with constant probability. Changing success rates or dependent trials require a different model.
Frequently Asked Questions
What is the expected number of trials?
For success probability p, the expected trial count is 1/p.
Can p exceed 1?
No.
Is it related to the negative binomial?
Yes. The geometric distribution is a special case focused on the first success.
Methodology, Assumptions and Interpretation
For a geometric model, probability depends on independent Bernoulli trials with constant success probability. Conventions differ on whether the variable counts trials until first success or failures before first success, so the definition must match the formula.