Definition:Classical Probability Model

Definition
Let $\EE$ be an experiment

The classical probability model on $\EE$ is a mathematical model that defines the probability space $\struct {\Omega, \Sigma, \Pr}$ of $\EE$ as follows:


 * $(1) \quad$ All outcomes of $\EE$ are equally likely


 * $(2) \quad$ There are a finite number of outcomes.

Then:


 * $\map \Pr {\text {event occurring} } := \dfrac {\paren {\text {number of outcomes favorable to event} } } {\paren {\text {total number of outcomes possible} } }$

or formally:


 * $\map \Pr \omega := \dfrac {\card \Sigma} {\card \Omega}$

where:


 * $\card {\, \cdot \,}$ denotes the cardinality of a set
 * $\omega$ denotes an event: $\omega \in \Omega$
 * $\Sigma$ denotes the event space: $\Sigma \subseteq \Omega$
 * $\Omega$ denotes the sample space.

Also see

 * Classical Probability is Probability Measure
 * De Méré's Paradox


 * Definition:Relative Frequency Model
 * Definition:Bayesian Probability Model