Two events A and B are (statistically) independent if the chance that they both happen simultaneously is the product of the chances that each occurs individually; i.e., if P(AB) = P(A)P(B). This is essentially equivalent to saying that learning that one event occurs does not give any information about whether the other event occurred too: the conditional probability of A given B is the same as the unconditional probability of A, i.e., P(A|B) = P(A). Two random variables X and Y are independent if all events they determine are independent, for example, if the event {a < X ≤ b} is independent of the event {c < Y ≤ d} for all choices of a, b, c, and d. A collection of more than two random variables is independent if for every proper subset of the variables, every event determined by that subset of the variables is independent of every event determined by the variables in the complement of the subset. For example, the three random variables X, Y, and Z are independent if every event determined by X is independent of every event determined by Y and every event determined by X is independent of every event determined by Y and Z and every event determined by Y is independent of every event determined by X and Z and every event determined by Z is independent of every event determined by X and Y.