Definition
Complement of an event
The complement of an event contains every possible outcome where that event does not happen.
Continue from this idea into connected AXIO math.
The event and its not-event fill the whole sample space with no overlap.
Boundary: The complement depends on the sample space. “Not red” means different outcomes if the possible colours change.
What it means
The complement is the “not” version of an event. First decide the full sample space, then remove every outcome in the event. Everything left belongs to the complement.
Remember it
The event and its not-event fill the whole sample space with no overlap.
Example
A spinner has equal sections numbered 1 to 8. Let A be “land on a multiple of 3,” so A = {3, 6}. The complement of A is {1, 2, 4, 5, 7, 8}. Its probability is 6/8 = 3/4.
Watch for
The complement depends on the sample space. “Not red” means different outcomes if the possible colours change.
Common mix-up
A complementary event is not an event that works well with another event; it is exactly the event “not A.”
Exact meaning
For an event A in a stated sample space, the complement of A contains exactly the outcomes not in A. The event and its complement do not overlap, together cover the sample space, and have probabilities that sum to 1.