Classical Probability#
When a given [[Experiments|experiment]] has a finite [[Experiments|sample space]] and each outcome is equally likely, there is a very natural way to form a [[Probability Spaces|probability space]] from it.
Definition: Classical Probability
Suppose we have an [[Experiments|experiment]] with a finite [[Experiments|sample space]] \(\Omega\) and let \(E\) be some [[Experiments|event]].
The classical probability of \(E\) is defined as the ratio of the total number of outcomes \(n\) in which \(E\) occurs to the total number of possible outcomes \(|\Omega|\):
\[ P(E) \overset{\text{def}}{=} \frac{n}{|\Omega|} \]