Probability & Combinatorics
Intermediate

Geometric Probability

Probability that the first success occurs on trial k.

Formula

P(X=k)=(1−p)k−1pP(X=k) = (1-p)^{k-1} p

Variables

pSuccess probability
kTrial number

Example

First head on 3rd flip: (0.5)²(0.5) = 0.125

Did You Know?

The geometric distribution is memoryless.

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