Classical Definition (A Priori) of Probability

Classical (a priori) definition -- Bernoulli's principle of equally likely outcomes. The basic assumption underlying the classical theory is that every outcome of the random experiment is equally likely. If an experiment has $n$ exhaustive, mutually exclusive, and equally likely outcomes, and $m$ of them are favourable to an event $A$, then the (classical, mathematical) probability of $A$ is defined as the ratio $\dfrac{m}{n}$. Formally (Definition 12.13):

where $n(S)$ and $n(A)$ are the number of elements of $S$ and $A$ respectively. This is the 'favourable over total' rule familiar from earlier study of frequency-based probability, now stated formally and given a precise underlying assumption. …