Apply and interpret the Addition Rule P(A or B)=P(A)+P(B)-P(A and B).
Use the Addition Rule to find P(A or B) for overlapping events
Problem
Use \(P(A~\text{or}~B)=P(A)+P(B)-P(A~\text{and}~B)\) with \(0.50\), \(0.30\), and overlap \(0.10\). Compute the union without double-counting the overlap.
Big Picture
What this problem is really about
Adding two event probabilities counts their shared outcomes twice, so the addition rule subtracts the overlap once. We’ll substitute both marginals and the intersection, perform the correction, and check that the inclusive union is at least each marginal but no larger than the uncorrected sum.
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