Geometric Distribution Calculator
Probability that the first success lands on trial k, plus P(X ≤ k), P(X > k), mean and variance of the geometric distribution.
How it works
P(X = k) = (1−p)^(k−1) · p · E[X] = 1/p · Var = (1−p)/p²
The geometric distribution counts independent trials until the first success. The first k−1 trials must fail (each with probability 1−p) and trial k must succeed. Its memoryless property means past failures never change the odds of the next trial.
Worked example
p = 0.2, k = 3: 0.8 × 0.8 × 0.2 = 0.128. P(success within 3 trials) = 1 − 0.8³ = 0.488.
Frequently asked questions
What about counting failures before the first success?
That version is shifted by one: P(Y = k) = (1−p)^k · p with mean (1−p)/p. Enter k+1 here to match it.
How is this different from binomial?
Binomial fixes the number of trials and counts successes; geometric fixes one success and counts trials.
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For education — check assumptions (sample size, distribution) before using statistics in real decisions.