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
Find \(P(A~\text{or}~B)\) by adding \(1/2\) and \(1/4\), then subtracting the shared overlap \(1/8\) once.
Big Picture
What this problem is really about
The addition rule corrects for double-counting when two events overlap. We’ll add the separate probabilities of A and B, subtract their shared probability exactly once, and simplify the resulting union fraction. Reconstructing the three disjoint Venn regions offers a check: A-only, overlap, and B-only should sum to the same inclusive-or probability.
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