Apply and interpret the Addition Rule P(A or B)=P(A)+P(B)-P(A and B).
Find a missing event probability using the Addition Rule
Problem
Rearrange the addition rule as \(P(A)=P(A~\text{or}~B)-P(B)+P(A~\text{and}~B)\), then substitute \(0.70\), \(0.30\), and \(0.10\).
Big Picture
What this problem is really about
Solving the addition rule for one marginal changes the overlap’s sign when it crosses the equation. We’ll isolate the missing event probability symbolically, substitute union, other marginal, and intersection, evaluate the signed operations, and plug the result back into the original rule.
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