The chain rule of probabilities states that the [[joint probability]] of a sequence of events is the product of the probabilities of each event given the preceding events have occurred. $P(X_1, X_2, X_3) = P(X_1) * P(X_2 | X_1) * P(X_3 | X_1, X_2)$ This simplifies calculation of joint probability when only conditional probabilities are provided as in an [[aggregation tree]].