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, called "success" and "failure." These last two words should not always be construed literally. Examples of Bernoulli trials include

• Flipping a coin. In this context, obverse ("heads") denotes success and reverse ("tails") denotes failure. A fair coin has the probability of success 0.5 by definition.
• Rolling a die, where for example we designate a six as "success" and everything else as 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.
• Call the birth of a baby of one sex "success" and of the other sex "failure." (Take your pick.)

Mathematically, such a trial is modeled by a random variable which can take only two values, 0 and 1, with 1 being thought off as "success". If p is the probability of success, then the expected value of such a random variable is p and its standard deviation is √(p(1-p)).

A Bernoulli process consists of repeatedly performing independent but identical Bernoulli trials, for instance flipping a coin 10 times.