Definition:Equiprobable Outcomes

Definition

Let $\struct {\Omega, \Sigma, \Pr}$ be a finite probability space.

Let $\Omega = \set {\omega_1, \omega_1, \ldots, \omega_n}$.

Suppose that $\map \Pr {\omega_i} = \map \Pr {\omega_j}$ for all the $\omega_i, \omega_j \in \Omega$.

$\forall \omega \in \Omega: \map \Pr \omega = \dfrac 1 n$
$\forall A \subseteq \Omega: \map \Pr A = \dfrac {\card A} n$

Such a probability space is said to have equiprobable outcomes, and is sometimes referred to as an equiprobability space.