Probability

Earlier classes introduced the frequency (a posteriori) definition of probability -- estimating $P(A)$ from how often $A$ actually occurred across many repeated trials. This chapter now builds up the theoretical machinery of probability from first principles, in two stages. First, Section 12.4.1 revisits the classical (a priori) definition, which assigns probabilities BEFORE any trial is run, purely from counting equally likely outcomes. Then Section 12.4.2 introduces the axiomatic approach, developed by A.N. Kolmogorov, which defines probability through a small set of rules (axioms) that any valid probability assi …