Complement of event A

Definition

The complement of event A, denoted as $A^c$ or $\overline{A}$, consists of all outcomes in the sample space that are not in event A. It is the opposite of event A happening.

5 Must Know Facts For Your Next Test

1. The probability of the complement of event A is calculated as $P(A^c) = 1 - P(A)$.
2. If event A is certain to happen, its complement will have a probability of 0.
3. If events A and B are mutually exclusive, then $P(A \cup B) = P(A) + P(B)$ includes the complements within their union logic.
4. The sum of probabilities for an event and its complement is always equal to 1.
5. In Venn diagrams, the complement of event A covers all areas outside circle A within the universal set.

Review Questions

• How do you represent the complement of an event in notation?
• What is the relationship between $P(A)$ and $P(A^c)$?
• What does it mean when $P(A^c) = 0$?

Related terms

Sample Space:

The set of all possible outcomes in a probability experiment.

Mutually Exclusive Events:

Two events that cannot occur at the same time.

$P(A \cup B)$: $P(A \cup B)$ represents the probability that either event A or event B or both occur.