Complement of an Event
Experiment 1: A spinner has 4 equal sectors colored yellow, blue, green and red. What is the probability of landing on a sector that is not red after spinning this spinner?
Sample Space: {yellow, blue, green, red}
Probability: The probability of each outcome in this experiment is one fourth. The probability of landing on a sector that is not red is the same as the probability of landing on all the other colors except red.
P(not red) 
= 
1 
+ 
1 
+ 
1 
= 
3 
4 
4 
4 
4 
In Experiment 1, landing on a sector that is not red is the complement of landing on a sector that is red.
Definition: The complement of an event A is the set of all outcomes in the sample space that are not included in the outcomes of event A. The complement of event A is represented by (read as A bar).
Rule: Given the probability of an event, the probability of its complement can be found by subtracting the given probability from 1.

P() = 1 – P(A) 
You may be wondering how this rule came about. In the last lesson, we learned that the sum of the probabilities of the distinct outcomes within a sample space is 1. For example, the probability of each of the 4 outcomes in the sample space above is one fourth, yielding a sum of 1. Thus, the probability that an outcome does not occur is exactly 1 minus the probability that it does. Let’s look at Experiment 1 again, using this subtraction principle.
Experiment 1: A spinner has 4 equal sectors colored yellow, blue, green and red. What is the probability of landing on a sector that is not red after spinning this spinner?
Sample Space: {yellow, blue, green, red}
Probability:
Experiment 2: A single card is chosen at random from a standard deck of 52 playing cards. What is the probability of choosing a card that is not a king?
Probability:
P(not king) 
= 
1 
– 
P(king) 
Experiment 3: A single 6sided die is rolled. What is the probability of rolling a number that is not 4?
Probability:
Experiment 4: A single card is chosen at random from a standard deck of 52 playing cards. What is the probability of choosing a card that is not a club?
Probability:
P(not club) 
= 
1 
– 
P(club) 
Experiment 5: A glass jar contains 20 red marbles. If a marble is chosen at random from the jar, what is the probability that it is not red?
Probability:
Note: This is an impossible event.
Summary: The probability of an event is the measure of the chance that the event will occur as a result of the experiment. The probability of an event A, symbolized by P(A), is a number between 0 and 1, inclusive, that measures the likelihood of an event in the following way:
 If P(A) > P(B) then event A is more likely to occur than event B.
 If P(A) = P(B) then events A and B are equally likely to occur.
 If event A is impossible, then P(A) = 0.
 If event A is certain, then P(A) = 1.
 The complement of event A is . P() = 1 – P(A)
Exercises
Directions: Read each question below. Select your answer by clicking on its button. Feedback to your answer is provided in the RESULTS BOX. If you make a mistake, choose a different button.
1. 
A glass jar contains 5 red, 3 blue and 2 green jelly beans. If a jelly bean is chosen at random from the jar, what is the probability that it is not blue? 




2. 
A student is chosen at random from a class of 16 girls and 14 boys. What is the probability that the student chosen is not a girl? 




3. 
A number from 1 to 5 is chosen at random. What is the probability that the number chosen is not odd? 




4. 
If a number is chosen at random from the following list, what is the probability that it is not prime?
2, 3, 5, 7, 11, 13, 17, 19 




5. 
If a single 6sided die is rolled, what is the probability of rolling a number that is not 8? 



