Complementary Events

Sometimes we need to find the probability that a single event A does not occur. 

The complement of A, denoted by A' and is read "A prime" or "A complement", consists of all outcomes in which A does not occur.

For example, if you roll a die and let E be the event that the number rolled is a 4 or higher, then the complement, E' is the event that the number rolled is a three or lower. In other words, E = {4, 5, 6} and E' = {1, 2, 3}.

Using the definition of the complement of an event and the fact that the sum of the probabilities of all outcomes is 1, you can come up with the following formulas:

$$P(E) + P(E') = 1$$        $$P(E) = 1 - P(E')$$        $$P(E') = 1 - P(E)$$

For more examples of how the complement rule is used in probability, watch the following video. In this video, instead of denoting the complement as A' she uses $$\bar{A}$$. Both notations are correct.

Last modified: Saturday, 3 February 2018, 4:31 PM