Complement of an Event
If event A is a subset of a sample space S, the complement of A contains the elements of S that are not members of A. The symbol for the complement of an event A is 
.
Example 1:
Consider the experiment of rolling a single die.
S = {1, 2, 3, 4, 5, 6}. Let A be the event that the roll yields a number greater than 4. A = {5, 6}. Then 
.
Remember: P(S) = 1. 
. Since A and are mutually exclusive, 
. Therefore, 
Example 2:
When it is not raining, the probability of the New Orleans Saints winning a football game is 
. What is the probability of the Saints winning if it is raining?
P(Saints winning with rain) = 1 – P(Saints winning without rain)
