Complement of an Event — Probability of "Not" (Grade 7)
The complement of an event is everything except that event. Since something either happens or it doesn't, P(event) + P(not event) = 1. So P(not event) = 1 − P(event). When "at least one" or "not" is easier to count the other way, the complement is a shortcut.
Understanding complement of an event
The complement of an event is everything except that event. Since something either happens or it doesn't, P(event) + P(not event) = 1. So P(not event) = 1 − P(event). When "at least one" or "not" is easier to count the other way, the complement is a shortcut.
Key Idea
The complement of an event is everything except that event. Since something either happens or it doesn't, P(event) + P(not event) = 1. So P(not event) = 1 − P(event). When "at least one" or "not" is easier to count the other way, the complement is a shortcut.
Seeing it in action
Worked example
A die: P(not rolling a 6)?
P(6) = 1/6. So P(not 6) = 1 − 1/6 = 5/6.
The complement is everything except the event.
Try a few
P(not heads) on a fair coin?
Spinner P(gold)=1/4 — P(not gold)?
P(not rolling a 1 or 2) on a die?
Spinner
A calm probability game for reading spinner sectors, fractions, complements, and comparisons.
Ready for the interactive lab?
Practice complement of an event in Numeris with instant feedback.
Put the reasoning on paper.
Try six fraction, angle, perimeter and area questions with explained answers, for grades 4–6.
Free printable · 3 pagesWant a printable set too?
Browse free math pages with separate student sheets and answer keys, or join our optional resource updates.
Looking for Grade 2 worksheets? →