SAT Math: Use the complement rule (P(not A) = 1 − P(A))
20+ practice questions in Praczo
The concept, explained
- 1
The complement rule: P(not A) = 1 − P(A). The probability that A does NOT happen is 1 minus the probability that it does.
- 2
Use the complement whenever it’s easier to count what you don’t want than what you do want — a common SAT shortcut.
- 3
The complement of "at least one" is "none." So P(at least one success) = 1 − P(no successes).
- 4
Complements apply to categorical outcomes too: P(not red) = 1 − P(red) even when there are multiple non-red categories.
- 5
Probabilities are between 0 and 1. If you compute 1 − P(A) and get a negative number, you used P(A) > 1, which means an earlier mistake.
- ✗ Forgetting to subtract from 1, especially on "at least one" problems — students sometimes subtract from total count instead of from 1.
- ✗ Confusing "complement" with "reciprocal" and computing 1/P(A) instead of 1 − P(A).
- ✗ Applying the complement rule to overlapping events when inclusion-exclusion is actually required.
SAT-style practice
A weather forecast says the probability of rain on Saturday is 0.35, and on Sunday is 0.40. If the two days are independent, what is the probability that it does NOT rain on either day?
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