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

See Also

What is probability?