Complement of an Event
If event is a subset of a sample space , the complement of contains the elements of that are not members of . The symbol for the complement of an event is .
Example 1:
Consider the experiment of rolling a single die.
. Let
be the event that the roll yields a number greater than
.
. Then
.
Remember: . , so . Since 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?
(Saints winning with rain)
= (Saints winning without rain)
=