# Definition:Classical Probability Model

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## 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

## Historical Note

The classical probability model arose when games of chance were first analyzed in the $17$th century, in the context of the gambling games of the European nobility.

Because of its assumption of equiprobable outcomes, this model is particularly useful when used in this context.

## Sources

- For a video presentation of the contents of this page, visit the Khan Academy.