Classical definition of probability

Definition

Let $\Omega$ be a nonempty finite set of equally likely outcomes. The classical probability of an event $A \subseteq \Omega$ is $$P(A) = \frac{|A|}{|\Omega|},$$ the number of favourable outcomes divided by the number of all outcomes.

Remarks

This $P$ is a probability measure on the power set of $\Omega$, the uniform probability on $\Omega$. Each outcome has probability $1/|\Omega|$. For two rolls of a fair die, the probability that the sum is $7$ is $6/36 = 1/6$. Classical probability turns a probability problem into a counting problem. Binomial coefficients and the rule of product often give the counts. The definition is circular as a foundation, since "equally likely" already uses probability. It also does not apply to infinite sample spaces.

Explanations

L1 human

When all outcomes have the same chance, a probability is a fraction: good cases over all cases. A fair die has $6$ faces and $3$ of them are even, so the chance of an even number is $3/6 = 1/2$.