Randomness is closely related to unpredictability of observation results and impossibility to predict them with sufficient accuracy. The nature of randomness is based on the lack of exhaustive information about the phenomenon under observation. As soon as you learn the origin of that phenomenon, you no longer consider it accidental or random. On the other hand, a random phenomenon whose origin has been revealed loses nothing of its random character. Randomness can be characterized as a type of relation stipulated by conditions that are inessential, superfluous, and extraneous to this particular phenomenon. Thus, the knowledge of the phenomenon is incomplete by definition.

Since our knowledge is incomplete, the observation results may prove impossible to predict with great accuracy. For instance, the initial state of the objects under observation may change imperceptibly for the used instruments, but these small changes may cause significant alterations in the final results. The sophisticated nature of the observed phenomenon may make accurate computation impossible in practice, if not in theory. Finally, even minor uncontrollable disturbing factors may cause serious deviations from a hypothetically "true value".

Although irregularities and deviations may occur, observational or experimental results still reveal a certain typical regularity called statistical stability. Various forms of statistical stability are formulated as specific rules that mathematical statistics calls laws of large numbers. This stability is the basis for the mathematical theory underlying the mathematical model of random phenomena. This theory is known as the theory of probability.