Determine event independence using P(A and B)=P(A)P(B).
Determine whether two events are independent by checking whether P(A and B) = P(A)P(B)
Problem
From the Venn regions, compute \(P(A)=30/100\), \(P(B)=40/100\), and \(P(A\cap{}B)=10/100\). Compare the joint probability with the product to test independence.
Venn marginals include each event’s exclusive region plus the overlap. We’ll compute both full event probabilities and the observed joint probability, multiply the marginals, and compare the two exact joint values to test independence without mistaking event-only counts for totals.
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