Complement of an event

Definition

The complement of an event is the set of all outcomes in a sample space that are not included in the event. It is denoted as $E'$ or $E^c$ where $E$ is the event.

5 Must Know Facts For Your Next Test

1. The probability of the complement of an event $P(E')$ is calculated as $1 - P(E)$.
2. If an event $E$ is certain to happen, then its complement $E'$ has a probability of 0.
3. If an event $E$ is impossible, then its complement $E'$ has a probability of 1.
4. The sum of the probabilities of an event and its complement always equals 1: $P(E) + P(E') = 1$.
5. The concept of complements is critical for understanding mutually exclusive events, where two events cannot both occur.

Review Questions

• How do you calculate the probability of the complement of an event?
• What is the relationship between the probabilities of an event and its complement?
• If an event has a probability of 0.3, what is the probability of its complement?

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.

$P(E)$: $P(E)$ denotes the probability that event $E$ occurs.