Classical definition of probability

The classical definition or interpretation of probability is identified with the works of Jacob Bernoulli and Pierre-Simon Laplace. As stated in Laplace's Théorie analytique des probabilités,

This definition is essentially a consequence of the principle of indifference. If elementary events are assigned equal probabilities, then the probability of a disjunction of elementary events is just the number of events in the disjunction divided by the total number of elementary events.

The classical definition of probability was called into question by several writers of the nineteenth century, including John Venn and George Boole. The frequentist definition of probability became widely accepted as a result of their criticism, and especially through the works of R.A. Fisher. The classical definition enjoyed a revival of sorts due to the general interest in Bayesian probability, because Bayesian methods require a prior probability distribution and the principle of indifference offers one source of such a distribution. Classical probability can offer prior probabilities that reflect ignorance which often seems appropriate before an experiment is conducted.

As a mathematical subject, the theory of probability arose very late—as compared to geometry for example—despite the fact that we have prehistoric evidence of man playing with dice from cultures from all over the world. One of the earliest writers on probability was Gerolamo Cardano. He perhaps produced the earliest known definition of classical probability.

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