A random number is generated by a random (stochastic) process such as throwing Dice. Individual numbers can't be predicted, but the likely result of generating a large quantity of numbers can be predicted by specific mathematical series and statistics.

Random numbers are frequently used in algorithms such as Knuth's 1964-developed algorithm^[1] for shuffling lists. (popularly known as the Knuth shuffle or the Fisher–Yates shuffle, based on work they did in 1938).

In 1999, a new feature was added to the Pentium III: a hardware-based random number generator.^[2][3] It has been described as "several oscillators combine their outputs and that odd waveform is sampled asynchronously."^[4] These numbers, however, were only 32 bit, at a time when export controls were on 56 bits and higher, so they were not state of the art.^[5]

In common understanding, "1 2 3 4 5" is not as random as "3 5 2 1 4" and certainly not as random as "47 88 1 32 41" but "we can't say authoritavely that the first sequence is not random ... it could have been generated by chance."^[6]

When a police officer claims to have done a "random .. door-to-door" search, there is a certain expectation that members of a jury will have.^{[7][8][example needed]}

Flaws in randomness have real-world consequences.^[9][10]

A 99.8% randomness was shown by researchers to negatively affect an estimated 27,000 customers of a large service^[9] and that the problem was not limited to just that situation.^{[clarification needed]}

• Algorithmically random sequence
• Quasi-random sequence
• Random number generation
• Random sequence
• Random variable
• Random variate
• Random real