Discussion
Probability of \((A \cup B) = P(A \cup B) =\)
Answer: B
\(P(A \cup B) = P(A) + P(B) - P(A \cap B)\), the addition rule of probability.
When the probabilities of A and of B are added, the outcomes in both events, \(A \cap B\), are counted twice. Subtracting \(P(A \cap B)\) once corrects the double count.
\(P(A) + P(B)\) alone is right only for mutually exclusive events, where \(P(A \cap B) = 0\). Adding \(P(A \cup B)\) again makes the formula circular and too large, and \(P(A)/P(B)\) has nothing to do with a union; a ratio of this kind appears in conditional probability.
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