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
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
Individual random events are by definition unpredictable, but in many cases the frequency of different outcomes over a large number of events is predictable.
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.
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.
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.
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.
This association facilitates the identification and the calculation of probabilities of the events.
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.
These and other constructs are extremely useful in probability theory and the various applications of randomness.
Randomness has many uses in science, art, statistics, cryptography, gaming, gambling, and other fields.
Randomness is most often used in statistics to signify well-defined statistical properties.
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.
By analogy, quasi-Monte Carlo methods use quasirandom number generators.
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.
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.
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.
Note that a random selection mechanism that selected 10 marbles from this bowl would not necessarily result in 1 red and 9 blue.
In situations where a population consists of items that are distinguishable, a random selection mechanism requires equal probabilities for any item to be chosen.
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.