The classical definition of probability is identified with the works of Pierre Simon Laplace. As stated in his Théorie analytique des probabilités ,

The probability of an event is the ratio of the number of cases favorable to it, to the number of all cases possible when nothing leads us to expect that any one of these cases should occur more than any other, which renders them, for us, equally possible.

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, in which the classical definition is seen as a special case of the more general Bayesian definition.

References

• Pierre-Simon de Laplace. Théorie analytique des probabilités. Paris: Courcier Imprimeur, 1812.

• Pierre-Simon de Laplace. Essai philosophique sur les probabilités, 3rd edition. Paris: Courcier Imprimeur, 1816.

• Pierre-Simon de Laplace. Philosophical essay on probabilities. New York: Springer-Verlag, 1995. (Translated by A.I. Dale from the fifth French edition, 1825. Extensive notes.)