Bernoulli Trial

In the theory of probability and statistics, a Bernoulli trial is an experiment whose outcome is random and can be either of two possible outcomes, "success" and "failure". The mathematical formalization of the Bernoulli trial is known as the Bernoulli process. This article offers an elementary introduction to the concept, whereas the article on the Bernoulli process offers a more advanced treatment.

In practice it refers to a single experiment which can have one of two possible outcomes. These events can be phrased into "yes or no" questions:

• Did the coin land heads?
• Was the newborn child a girl?

Therefore success and failure are labels for outcomes, and should not be construed literally. The term "success" in this sense consists in the result meeting specified conditions, not in any moral judgement. Examples of Bernoulli trials include

• Flipping a coin. In this context, obverse ("heads") conventionally denotes success and reverse ("tails") denotes failure. A fair coin has the probability of success 0.5 by definition.
• Rolling a die, where a six is "success" and everything else a "failure".
• In conducting a political opinion poll, choosing a voter at random to ascertain whether that voter will vote "yes" in an upcoming referendum.