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 events of a particular type in some reference class of events.

Symbolically:


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

where:


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

Many sources adopt a slightly different definition as a limit that such a frequency converges to, were the number of observations to approach infinity. According to this definition,


 * $\Pr \left({\omega}\right) := \displaystyle \lim_{n \to \infty}\dfrac f n$

and:


 * $\Pr \left({\omega}\right) \approx \dfrac f n$

for large $n$. 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
 * Classical Probability Model