Apply and interpret the Addition Rule P(A or B)=P(A)+P(B)-P(A and B).
Find P(A and B) from P(A), P(B), and P(A or B) using the Addition Rule
Problem
Rearrange the addition rule as \(P(A~\text{and}~B)=P(A)+P(B)-P(A~\text{or}~B)\), then substitute \(0.60\), \(0.50\), and \(0.80\).
Big Picture
What this problem is really about
The overlap can be recovered by rearranging the addition rule before inserting numbers. We’ll isolate the intersection as the sum of marginals minus the union, substitute in that order, and check that the result is nonnegative and no greater than either individual event probability.
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