Probability of complementary events

In this lesson, you will learn to compute the probability of complementary events. What are complementary events though?

Let A be an event. The complement of A consists of all outcomes in which event A does not occur.

The symbol that we use to denote the complement of A is A

A and  the complement of A are called complementary events

Sometimes, we need to compute the probability that an event A occur and the probability that event A does not occur.

For example, company x conducted a survey to find out whether or not cars built in the 1970 had defects in the engine.

The result revealed that 4 out of every 100 cars had a defect in the engine. What are the probabilities of the two complementary events?

The two complementary events for this experiment are the following:

Let A = the car selected has a defect in the engine.

Let A = the car selected does not have a defect in the engine.

Here are the probabilities

P(A) =
4 / 100
= 0.04

P(A) =
96 / 100
= 0.96

Notice that 0.04 + 0.96  = 1

In general the probability of complementary events will add up to 1.

P(A) + P(A) = 1

Notice also that event A and the complement of event A are mutually exclusive. This means that event A and the complement of event A have nothing in common.

This makes sense since it is not possible for a car to have a defect and not have a defect at the same time.

We can conclude that two complementary events are always mutually exclusive.

Recent Articles

  1. How To Find The Factors Of 20: A Simple Way

    Sep 17, 23 09:46 AM

    Positive factors of 20
    There are many ways to find the factors of 20. A simple way is to...

    Read More

  2. The SAT Math Test: How To Be Prepared To Face It And Survive

    Jun 09, 23 12:04 PM

    SAT math
    The SAT Math section is known for being difficult. But it doesn’t have to be. Learn how to be prepared and complete the section with confidence here.

    Read More

Tough algebra word problems

100 Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Math quizzes


Math vocabulary quizzes