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**Randomness is the lack of pattern or predictability in events. **

Predictability is the degree to which a correct prediction or forecast of a system's state can be made either qualitatively or quantitatively.

A pattern, apart from the term's use to mean "template", is a discernible regularity in the world or in a manmade design.

What is Random? by Vsauce

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**A random sequence of events, symbols or steps has no order and does not follow an intelligible pattern or combination. **

A symbol is a mark, sign, or word that indicates, signifies, or is understood as representing an idea, object, or relationship.

Randomness by ZooshExtras

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**Individual random events are by definition unpredictable, but in many cases the frequency of different outcomes over a large number of events is predictable. **

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**For example, when throwing two dice, the outcome of any particular roll is unpredictable, but a sum of 7 will occur twice as often as 4. In this view, randomness is a measure of uncertainty of an outcome, rather than haphazardness, and applies to concepts of chance, probability, and information entropy.
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Information entropy is the average rate at which information is produced by a stochastic source of data.

Dice are small throwable objects with multiple resting positions, used for generating random numbers.

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**The fields of mathematics, probability, and statistics use formal definitions of randomness. **

Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.

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**In statistics, a random variable is an assignment of a numerical value to each possible outcome of an event space. **

In probability and statistics, a random variable, random quantity, aleatory variable, or stochastic variable is a variable whose possible values are outcomes of a random phenomenon.

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**This association facilitates the identification and the calculation of probabilities of the events. **

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**Random variables can appear in random sequences. **

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**A random process is a sequence of random variables whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions. **

In probability theory and statistics, a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a collection of random variables.

Determinism is the philosophical theory that all events, including moral choices, are completely determined by previously existing causes.

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**These and other constructs are extremely useful in probability theory and the various applications of randomness.
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Randomness has many uses in science, art, statistics, cryptography, gaming, gambling, and other fields.

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**Randomness is most often used in statistics to signify well-defined statistical properties. **

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**Monte Carlo methods, which rely on random input, are important techniques in science, as, for instance, in computational science. **

Monte Carlo methods are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results.

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**By analogy, quasi-Monte Carlo methods use quasirandom number generators.
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Random number generation is the generation of a sequence of numbers or symbols that cannot be reasonably predicted better than by a random chance, usually through a hardware random-number generator.

In numerical analysis, the quasi-Monte Carlo method is a method for numerical integration and solving some other problems using low-discrepancy sequences.

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**Random selection, when narrowly associated with a simple random sample, is a method of selecting items from a population where the probability of choosing a specific item is the proportion of those items in the population. **

In statistics, a simple random sample is a subset of individuals chosen from a larger set.

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**For example, with a bowl containing just 10 red marbles and 90 blue marbles, a random selection mechanism would choose a red marble with probability 1/10. **

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**Note that a random selection mechanism that selected 10 marbles from this bowl would not necessarily result in 1 red and 9 blue. **

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**In situations where a population consists of items that are distinguishable, a random selection mechanism requires equal probabilities for any item to be chosen. **

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**That is, if the selection process is such that each member of a population, of say research subjects, has the same probability of being chosen then we can say the selection process is random.**