Definition
Classical probability defines the probability of an event as the number of outcomes favourable to that event divided by the total number of equally-likely outcomes. For a fair die, the probability of rolling an even number is 3/6 = 1/2 because three of the six equally-likely faces are even.
This is the oldest formal interpretation, developed in the 17th and 18th centuries by Pascal, Fermat, and codified by Laplace. It works beautifully for symmetric games of chance — coins, dice, cards, roulette — but breaks down whenever outcomes are not naturally equally likely.
Why it matters
How it works
To compute a classical probability, you first list the sample space — the set of equally-likely outcomes. Then you count how many of those outcomes belong to the event of interest, and divide. The hard part is usually the counting, which is why combinatorics (permutations, combinations, partitions) is central to classical probability.
For example, the probability of being dealt a flush in a five-card poker hand is the number of flush hands divided by the total number of five-card hands, both computed via binomial coefficients.