In the Addition Rule ($P(A \cup B) = P(A) + P(B) - P(A \cap B)$), why is the probability of the intersection subtracted?
Answer
To avoid double-counting the outcomes that belong to both events.
When adding the probabilities of A and B separately, any outcome shared by both events (the intersection) is counted twice; subtracting the probability of the intersection corrects this duplication.
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