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." The word probability derives from the Latin probare (to prove, or to test). ... An example of statistics used in educational assessment. ...

In practice it refers to a single event which can have one of two possible outcomes. These events can be phrased into "yes or no" questions. For example: An event is something that takes place; an occurrence and arbitrary point in time. ...

• Will the coin land heads?
• Was the newborn child a girl?
• Are a person's eyes green?
• Did a mosquito die after the area was sprayed with insecticide?
• Did a potential customer decide to buy my product?
• Did a citizen vote for a specific candidate?
• Is this employee going to vote pro-union?

Therefore 'success' and 'failure' are labels for outcomes, and should not be construed literally. Examples of Bernoulli trials include: word coinage Coín (a town in Malaga province in Spain) 25¢ Canadian coin A coin is usually a piece of hard material, generally metal and usually in the shape of a disc, which is issued by a government to be used as a form of money. ...

• 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 dice, 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.

Mathematically, such a trial is modeled by a random variable which can take only two values, 0 and 1, with 1 being thought of 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 Coin flipping or coin tossing is the practice of throwing a coin in the air to resolve a dispute between two parties. ... A random variable can be thought of as the numeric result of operating a non-deterministic mechanism or performing a non-deterministic experiment to generate a random result. ... In probability theory (and especially gambling), the expected value (or mathematical expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff (value). Thus, it represents the average amount one expects to win per bet if bets with identical... In probability and statistics, the standard deviation is the most commonly used measure of statistical dispersion. ...

A Bernoulli process consists of repeatedly performing independent but identical Bernoulli trials, for instance flipping a coin 10 times. In probability and statistics, a Bernoulli process is a discrete_time stochastic process consisting of finite or infinite sequence of independent random variables X1, X2, X3,..., such that For each i, the value of Xi is either 0 or 1; For all values of i, the probability that Xi = 1 is...

See also: Bernoulli distribution. In probability theory and statistics, the Bernoulli distribution, named after Swiss scientist James Bernoulli, is a discrete probability distribution, which takes value 1 with success probability and value 0 with failure probability . ...