"The mathematical theory of probability arose from attempts to formulate mathematical descriptions of chance events, originally in the context of gambling, but later in connection with physics. Statistics is used to infer the underlying probability distribution of a collection of empirical observations. For the purposes of simulation, it is necessary to have a large supply of random numbers or means to generate them on demand."
"Randomness versus unpredictability.
Randomness, as opposed to unpredictability, is held to be an objective property -determinists believe it is an objective fact that randomness does not in fact exist. Also, what appears random to one observer may not appear random to another."
"Closely connected, therefore, with the concepts of chance, probability, and information entropy, randomness implies a lack of predictability. More formally, in statistics, a random process is a repeating process whose outcomes follow no describable deterministic pattern, but follow a probability distribution, such that the relative probability of the occurrence of each outcome can be approximated or calculated. For example, the rolling of a fair six-sided die in neutral conditions may be said to produce random results, because one cannot compute, before a roll, what number will show up. However, the probability of rolling any one of the six rollable numbers can be calculated, assuming that each is equally likely."
http://en.wikipedia.org/wiki/Randomness
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