# Statistics/Probability/Bernoulli Trials

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A lot of experiments just have two possible outcomes, generally referred to as "success" and "failure". If such an experiment is independently repeated we call them (a series of) **Bernoulli trials**. Usually the probability of success is called p. The repetition may be done in several ways:

- a fixed number of times (n); as a consequence the observed number of successes is stochastic;
- until a fixed number of successes (m) is observed; as a consequence the number of experiments is stochastic;

In the first case the number of successes is Binomial distributed with parameters n and p. For n=1 the distribution is also called the Bernoulli distribution. In the second case the number of experiments is Negative Binomial distributed with parameters m and p. For m=1 the distribution is also called the Geometric distribution.