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In common usage, randomness is the apparent or actual lack of pattern or predictability in events. [1] [2] A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual random events are, by definition, unpredictable, but if the probability distribution is known, the frequency of different outcomes over repeated events (or "trials") is predictable. [note 1] For example, when throwing two dice , the outcome of any particular roll is un

The fields of mathematics, probability, and statistics use formal definitions of randomness. In statistics, a random variable is an assignment of a numerical value to each possible outcome of an event space . This association facilitates the identification and the calculation of probabilities of the events. Random variables can appear in random sequences . A random process is a sequence of random variables whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability

Randomness is most often used in statistics to signify well-defined statistical properties. Monte Carlo methods , which rely on random input (such as from random number generators or pseudorandom number generators ), are important techniques in science, particularly in the field of computational science . [3] By analogy, quasi-Monte Carlo methods use quasi-random number generators .

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