Apply and interpret the general Multiplication Rule with conditional probability.
Find a joint probability from a marginal probability and a conditional probability
Problem
Calculate \(P(A~\text{and}~B)\) by multiplying \(P(A)=1/3\) by \(P(B|A)=3/5\) and simplifying.
Big Picture
What this problem is really about
The multiplication rule builds a joint probability from one event’s marginal and the other event’s conditional rate within it. We’ll use A as the first-stage probability, multiply by B’s rate among A outcomes, and reduce the product. Dividing the joint result by A’s nonzero marginal should recover the supplied conditional factor.
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