Applied Mathematics

Probability Theory

What are the multiplication rules of probability?

In probability theory, the multiplication rule is used to determine the probability that two events, A and B, both occur. As with the addition rules, the notation for multiplication rules of probability are most commonly seen in terms of sets: P(AB) = P(A|B) • P(B) or P(AB) = P(B|A) • P(A), in which P(A) represents the probability that event A will occur, P(B) represents the probability that event B will occur, and P (AB) is translated as the probability that event A and event B will both occur. In addition, P(A|B) is the conditional probability that event A occurs given that event B has already occurred, and P(B A) is the conditional probability that event B occurs given that event A has already occurred. Similar to the addition rules, if there are independent events (or those that have no influence on one another), the equation reduces to P(AB) = P(A) • P(B).



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