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.
Understanding complement of an event
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.
A common mistake, and the fix
Subtracting from the wrong whole.
P(not a 6) = 1 − 1/6 = 5/6, the five faces 1 to 5. A probability’s whole is 1, so “6 − 1/6” or “1 − 6” can’t be right.
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?
four faces, 3 to 6, out of 6.
Spinner
A calm probability game for reading spinner sectors, fractions, complements, and comparisons.
Try it in Numeris.
A short lesson, then practice with feedback on every answer.
Want more practice?
Practise this skill in Numeris, browse more free math pages, or join our optional resource updates.
All free math pages →