Classical Probability

When a given experiment has a finite sample space and each outcome is equally likely, there is a very natural way to form a probability space from it.

Definition: Classical Probability

Suppose we have an experiment with a finite sample space $\Omega$ and let $E$ be some 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 $|\Omega |$:

$$P(E)\stackrel{\text{def}}{=}\frac{n}{|\Omega |}$$

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