Complement

Definition

The complement of an event A in probability is the set of all outcomes in the sample space that are not in A. It is often denoted as $A^c$ or $\overline{A}$.

5 Must Know Facts For Your Next Test

1. The probability of the complement of an event A, denoted $P(A^c)$, is calculated as $1 - P(A)$.
2. If $P(A)$ is known, finding $P(A^c)$ can be a quick way to solve probability problems.
3. The sum of the probabilities of an event and its complement is always equal to 1: $P(A) + P(A^c) = 1$.
4. Complementary events are mutually exclusive; they cannot happen at the same time.
5. Understanding complements can simplify complex probability questions by focusing on what does not happen.

Review Questions

• How do you calculate the probability of the complement of an event A?
• What is the relationship between $P(A)$ and $P(A^c)$?
• Why are complementary events considered mutually exclusive?

Related terms

Sample Space:

The set of all possible outcomes in a probability experiment.

Mutually Exclusive Events:

Events that cannot occur at the same time.

Probability:

A measure quantifying the likelihood that events will occur, ranging from 0 to 1.