basic

Geometric Distribution First-Success Trial Calculator

P(X=k) = (1−p)^(k−1)·p — first success on trial k.

Calculates the probability of achieving the first success on exactly the k-th trial in a geometric distribution, plus mean and variance.

Marcus Laurent By Marcus Laurent
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

P(X=k) = (1−p)^(k−1) × p; E[X] = 1/p

In depth

Calculates the probability of achieving the first success on exactly the k-th trial in a geometric distribution, plus mean and variance.