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Why does the addition rule subtract the probability of A and B?
ATo stop outcomes in both events being counted twice
BTo stop the total from ever falling below zero
CTo turn the union into an intersection instead
DTo make the two events mutually exclusive first
Answer & Solution
Correct answer: A. To stop outcomes in both events being counted twice
1. Outcomes that belong to both A and B appear in each of the two separate probabilities.
2. Simply adding the probabilities therefore counts those outcomes twice.
3. Subtracting the joint probability once removes the duplicate count and leaves the correct union.
_Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 3 "Probability Topics", section 3.3 Two Basic Rules of Probability_
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