# What Is a Complementary Event?

## What Is a Complementary Event?

The complement of an event in probability is all outcomes that are not the event.

## A Real Example of Complementary Events

It is easier to understand complementary events with an example.

### Tossing a Coin

If a coin is tossed, the coin can land on **Heads**.

The complement to this event is the event where the coin does **not** land on **Heads**.

If the coin does not land on **Heads**, it must land on **Tails**.

**Tails** is the event **not Heads**. **Tails** is the complement to the event **Heads**.

**Heads** is the event **not Tails**. **Heads** is the complement to the event **Tails**.

Together, **Heads** and **Tails** are complementary events for the toss of a coin.

## The Complement Rule

The probability of complementary events sum to 1:

Probability of event happening + Probability of event not happening = 1

Therefore:

Probability of event happening = 1 − Probability of event not happening

Probability of event not happening = 1 − Probability of event happening