Definition:Equiprobable Outcomes

Definition

Let $\left({\Omega, \Sigma, \Pr}\right)$ be a finite probability space.

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

Suppose that $\Pr \left({\omega_i}\right) = \Pr \left({\omega_j}\right)$ for all the $\omega_i, \omega_j \in \Omega$.

Then from Probability Measure on Equiprobable Outcomes:

• $\displaystyle \forall \omega \in \Omega: \Pr \left({\omega}\right) = \frac 1 n$
• $\displaystyle \forall A \subseteq \Omega: \Pr \left({A}\right) = \frac {\left|{A}\right|} n$

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

Sources

• Geoffrey Grimmett: Probability: An Introduction (1986): $\S 1.5$: Example $17$