# Successes and Failures in a Run of Bernoulli Trials

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Bernoulli trials are independent and their probability of success on each trial is a constant value, say . If is the number of successes in a run of Bernoulli trials, then is a binomial random variable with parameters and . If is the number of failures in the same sequence of trials, then is also a binomial random variable, but with parameters and . Any event expressed in terms of the number of successes can also be expressed in terms of the number of failures; for example, more than three successes is the same as fewer than failures.

Contributed by: Chris Boucher (March 2011)

Open content licensed under CC BY-NC-SA

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"Successes and Failures in a Run of Bernoulli Trials"

http://demonstrations.wolfram.com/SuccessesAndFailuresInARunOfBernoulliTrials/

Wolfram Demonstrations Project

Published: March 7 2011