Definition:Classical Probability Model

Definition

The classical probability model is a mathematical model that defines the probability of an event occurring as follows:

$\Pr\left(\text{event occuring}\right) := \dfrac {\left( \text {number of outcomes favorable to event}\right)}{\left( \text{total number of outcomes possible}\right)}$

or formally:

$\Pr \left({\omega}\right) := \dfrac {\# \left({\Sigma}\right)} {\# \left({\Omega}\right)}$

where:

• $\#$ is the cardinality of a set
• $\omega$ is an event
• $\Sigma$ is the event space
• $\Omega$ is the sample space.

This model assumes that all outcomes of the experiment are equally likely and that there are a finite number of outcomes.

The classical probability model is a probability measure, proved here.

Also see

• Classical Probability is a Probability Measure
• De Méré's Paradox
• Relative Frequency Model
• Bayesian Probability Model

Comment

Because of its assumption of equiprobable outcomes, this model is particularly useful when analyzing games of chance. Indeed, the birth of probability theory is closely tied to the gambling games of the seventeenth century European nobility.

Sources

• http://grove.ufl.edu/~fass/Exam%20P%20Study%20Guide.pdf $\S 6$
• For a video presentation of the contents of this page, visit the Khan Academy.