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.
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