Complement Probability Calculator
Find the complement P(not A) = 1 − P(A), plus the odds for and against an event, from a single probability.
How it works
P(not A) = 1 − P(A) · odds against = P(not A) : P(A)
Every event and its complement partition all outcomes, so their probabilities must sum to exactly one. The complement rule is the workhorse behind “at least one” problems: it is almost always easier to compute the chance something does not happen and subtract. Odds simply re-express the same information as a ratio of the two probabilities.
Worked example
If P(A) = 30%, then P(not A) = 1 − 0.30 = 70%. The odds against A are 0.70 : 0.30, which simplifies to about 2.33 : 1.
Sources: Complementary event — Wikipedia
Frequently asked questions
Why do probabilities of complements add to one?
Because A and “not A” together cover every possible outcome with no overlap. Their probabilities therefore fill the entire sample space, which has total probability one.
How do I turn probability into odds?
Odds against are P(not A) : P(A). A 30% probability gives 70 : 30, or roughly 2.33 to 1 against.
When is the complement most useful?
Whenever the direct event is a messy union — especially “at least one” questions. Computing the single “none” case and subtracting from one is far quicker.
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This calculator is for educational purposes. Double-check important results before acting on them.