Definition:Relative Frequency Model

Definition

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

$\Pr \left({\text{event occurring}}\right) := \dfrac {\left({\text {observed number of times event has occurred in the past}}\right)} {\left({\text{observed number of times event has occurred or not occurred}}\right)}$

That is, the probability of an event happening is defined as the relative frequency of a finite number of events of a particular type in some finite reference class of events.

Symbolically:

$\Pr \left({\omega}\right) := \dfrac f n$

where:

• $\omega$ is an event
• $f$ is how many times $\omega$ occured
• $n$ is the number of trials observed.

Many sources adopt a slightly different perspective as an underlying constant that such a frequency converges to, were the number of observations to approach infinity. According to this approach, it may be impossible to find out the "true" probability of an event. The model as defined above, then, is an approximation.

Either way, the assumption is that were we to conduct a large number of trials, the frequency of events occurring in the new experiments should be roughly equal to the frequency of events occurring in the observed cases.

The relative frequency model is a probability measure, proved here.

Also see

• Relative Frequency is a Probability Measure
• Bayesian Probability Model
• Classical Probability Model

Sources

• Michael C. Gemignani: Calculus and Statistics (1970) $\S 1.3$
• Merrilee H. Salmon: Introduction to Logic and Critical Thinking (1995) $\S 6.1$
• Michael A. Bean: Probability: The Science of Uncertainty (2001) $\S 1.2$
• 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.