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:
P(not red)
=
1
-
P(red)
=
1
-
1
4
=
3
4
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)
=
1
-
4
52
=
48
52
=
12
13
Experiment 3:
A single 6-sided die is rolled. What is the probability of rolling a
number that is not 4?
Probability:
P(not 4)
=
1
-
P(4)
=
1
-
1
6
=
5
6
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)
=
1
-
13
52
=
39
52
=
3
4
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:
P(not red)
=
1
-
P(red)
=
1
-
1
=
0
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 6-sided die is rolled, what is the probability of rolling a number that is not 8?
Interactive Math Goodies Software
(read as A bar).
![[IMAGE]](images/poker_hand.gif)
![[IMAGE]](images/red_marbles.gif)
