Independence

Two events are independent when knowing that one happened tells you nothing about whether the other happens, so P(A given B) equals P(A). Successive fair coin flips are the canonical example: a run of five heads does not make tails “due” on the sixth flip.

Independence lets you multiply probabilities (P(A and B) = P(A) × P(B)), which simplifies almost every calculation and underlies many models. The danger is assuming independence when it does not hold; correlated events, like rain on consecutive days, violate it and make the simple multiplication wrong.