Complement rule
SAT glossary · Math
Definition
P(not A) = 1 - P(A), since everything either happens or does not. Deploy it whenever 'at least one' appears — the opposite of 'at least one' is 'none,' which is usually far easier to count, and the complement route is faster whenever the 'not' set is bigger.
Complement rule in plain English
The complement of an event is simply 'everything that ISN'T that event' — and since something always either happens or doesn't, the probability of an event plus the probability of it NOT happening must add up to exactly 1 (100%). That gives you the shortcut P(not A) = 1 - P(A). This becomes a genuine timesaver whenever a question uses the phrase 'at least one,' because the opposite of 'at least one thing happens' is 'literally nothing happens' — which is usually way easier to calculate directly. So instead of adding up a dozen different ways something could happen at least once, you calculate the one easy way it could happen ZERO times, and subtract that from 1.
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