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
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.