# Equiprobability

Equiprobability is a property for a collection of events that each have the same probability of occurring. In statistics and probability theory it is applied in the discrete uniform distribution and the equidistribution theorem for rational numbers. If there are ${\textstyle n}$ events under consideration, the probability of each occurring is ${\textstyle {\frac {1}{n}}.}$ In philosophy it corresponds to a concept that allows one to assign equal probabilities to outcomes when they are judged to be equipossible or to be "equally likely" in some sense. The best-known formulation of the rule is Laplace's principle of indifference (or principle of insufficient reason), which states that, when "we have no other information than" that exactly $N$ mutually exclusive events can occur, we are justified in assigning each the probability ${\textstyle {\frac {1}{N}}.}$ This subjective assignment of probabilities is especially justified for situations such as rolling dice and lotteries since these experiments carry a symmetry structure, and one's state of knowledge must clearly be invariant under this symmetry.