Determine event independence using P(A and B)=P(A)P(B).
Determine whether two events are independent using \(P(A and B) = P(A)P(B)\)
Problem
Are events \(A\) and \(B\) independent? Use these probabilities: \(P(A)=1/2\), \(P(B)=1/3\), \(P(A~\text{and}~B)=1/6\).
Big Picture
What this problem is really about
Independence is tested by comparing the joint probability with the product of the two marginal probabilities. We’ll multiply the given fractions, simplify the product, place it beside the observed intersection probability, and classify the events from exact equality rather than relative size.
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