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.


This Demonstration provides answers to the following questions: (1) for an event of given probability, how many trials, on average, does it take for a successful result?; and (2) what is the probability of a given number of trials before a success?


Contributed by: Daniel Tokarz (August 2016)
Open content licensed under CC BY-NC-SA



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

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