The Multiplication Rule

Probability · Axiom Academy

LESSON The Multiplication Rule Finding the probability of joint events using conditional probability 1. Deriving the Multiplication Rule Starting from the conditional probability formula P(A|B) = P(A∩B)/P(B), we can multiply both sides by P(B) to isolate the intersection. The multiplication rule has two equivalent forms, depending on which event we condition on. Both are equally valid and give the same result. 3. Visualizing with Tree Diagrams Tree diagrams show sequential events where we first determine if B occurs, then determine if A occurs. Probabilities along each path multiply together. 4. Application to Sequential Experiments When events occur in sequence, the multiplication rule is particularly natural. The outcome of the first event affects the probability of the second event.

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