Equiprobable

Equiprobable refers to a set of outcomes in a probabilistic experiment that are all equally likely to occur. In a discrete finite sample space, equiprobability means every elementary outcome has the same probability.

If the sample space Ω contains n outcomes and P(ω) is the probability of outcome ω, then equiprobability means P(ω) = 1/n for all ω in Ω, and the probability of any event A ⊆ Ω is P(A) = |A|/n.

Examples include rolling a fair six-sided die, where Ω = {1,2,3,4,5,6} and P({k}) = 1/6 for each k; drawing a card from a well-shuffled standard deck, where each of the 52 cards is equally likely; and flipping a fair coin, with outcomes Heads and Tails each having probability 1/2.

For continuous random variables, the concept is related to the uniform distribution; a continuous uniform distribution assigns equal probability density over an interval, but the probability of any single point is zero, so equiprobability of individual outcomes is not applicable in the same way.

Equiprobable models are an idealization; in practice choices may be biased due to physical imperfections or design. When outcomes are not equiprobable, probabilities must be assigned according to relative frequencies or a specified weighting. The assumption of equiprobability underlies simple counting principles: the probability of an event is the ratio of favorable outcomes to the total number of outcomes.