Complement Rule
GMAT glossary · Playbook
Definition
P(event) = 1 - P(complement), especially powerful when at-least-one language makes the opposite smaller to count.
Complement Rule in plain English
Use the Complement Rule when at least one / none language makes the complement smaller. Clues include at least one, none of, or probability of not. Blueprint: P(event) = 1 - P(complement). Expanding at-least-one into disjoint unions is longer than one complement, especially as the number of trials grows. Prefer this whenever the opposite event is a single clean case such as all failures. Micro-example: chance of at least one heads in two fair flips. Complement is two tails = 1/4, so P(at least one heads) = 1 - 1/4 = 3/4, skipping the HH/HT/TH case list entirely. The same move works in counting form: count total outcomes, subtract the all-fail outcomes, and skip the long at-least-one expansion.
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