# Probability in a Geometric Distribution

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A geometric distribution models the probability that an event with a given *a priori* probability achieves its first success after trials. For an event with probability , the expected number of trials before a success is , and the probability that the success occurs at trial is . The probability that the success occurs in a given range (with selected minimum and maximum) can be found by summing these probabilities.

Contributed by: Daniel Tokarz (August 2016)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Snapshot 1: even with a small probability of success, there is only a small chance that 30 trials will occur before a success

Snapshot 2: with a very large probability of success, there is a tiny chance of four or more trials without a success

Snapshot 3: with a probability of 1/2, there is a 3/4 chance of a success in the first two trials

## Permanent Citation

"Probability in a Geometric Distribution"

http://demonstrations.wolfram.com/ProbabilityInAGeometricDistribution/

Wolfram Demonstrations Project

Published: August 8 2016