Name ___________________
Probability, Averages, and Counting Techniques
Probability:
# of favorable outcomes
# of total outcomes
Ex. 1 Billy has a container filled with jellybeans. It contains 4 red beans, 5 green beans, and 3 yellow
beans. What is the probability that Billy will reach in without looking and pull out a red jelly bean?
Probability of an Event NOT Happening: 1 – probability of an event happening
Ex. 2 Billy has a container filled with jellybeans. It contains 4 red beans, 5 green beans, and 3 yellow
beans. What is the probability that Billy will reach in without looking and pull out any color other than
yellow?
Ex. 3 If the probability of an event occurring is
3
, what is the probability of the event NOT occurring?
5
Compound Events: Multiply the probabilities together
Ex. 4 Jan is flipping a fair coin and rolling a number cube with sides labeled 1 – 6. What is the
probability that the coin will land on tails and the number cube will roll a four?
Ex. 5 Billy has a container filled with jellybeans. It contains 4 red beans, 5 green beans, and 3 yellow
beans. What is the probability that Billy will reach in without looking and pull out a green jelly bean and
then pull out another green jelly bean WITHOUT replacing the first one? LEAVE YOUR ANSWER AS
A REDUCED FRACTION (MATH – ENTER – ENTER)!
Fundamental Counting Principle: Multiply the choices together
Ex. 6 At a restaurant, you can choose from 6 different appetizers, 4 different dinners, and 5 different
desserts. How many different meals can you create if you always choose one appetizer, one dinner, and
one dessert?
Ex. 7 The Science Club is going to select one of its 25 members to be President, one to be Vice President,
and one to be the Treasurer. Which of the following calculations will provide the number of ways that the
officers could be selected?
A.
25  25  25
B. 25  24  23
C. 25 3
D. 25  25  25
E. Cannot be determined
Timing Overlap: Look for the LEAST COMMON MULTIPLE
Ex. 8 Doug has to take two different medications for his cold. One pill is to be taken every 4 hours, and
the other is to be taken every 6 hours. If he just took both pills, how many hours will pass before he takes
both pills at the same time again?
A.
B.
C.
D.
E.
2
4
6
12
24
Ex. 9 Two security officers patrol the same building but at different times. John makes a security sweep
every 30 minutes and Diane makes a security sweep every 45 minutes. They both just ran a security
sweep together. How many minutes will pass before they run a sweep together again?
A.
B.
C.
D.
E.
5
30
45
90
1350
Averages: Add up all data values and divide by the number of values
Ex. 10 Joe went bowling last night and scored 124, 145, and 113. What is his average bowling score?
Ex. 11 Marissa has taken four math tests so far this year and scored 89, 95, 92, and 88. What will she
have to score on her fifth and final test to average 90?
A.
B.
C.
D.
E.
83
86
90
91
Cannot be determined
Name ___________________________
Probability, Averages, and Counting Techniques PRACTICE A
1. You tossed a fair coin 10 times, recording H when the head side landed up and T when the tail side
landed up. You recorded: T H H H H T H H H H. What is the probability that the head side will land
up on your next toss?
F.
0
G.
1
 
2
1
H.  
2
1
J.
2
K.
11
9
1
2. At a dog show, there are 4 poodles, 5 Labrador retrievers, 2 boxers, and 3terriers. If all dogs have an
equally likely chance of winning, what is the probability that a poodle will win?
3. Using the same information from #3, what is the probability that anything other than a terrier will
win?
4. Using the same information from #3, you have to select a team of dogs to tour the country. You must
choose one poodle, one Labrador retriever, one boxer, and one terrier. How many different teams can
you choose?
SHOW WHAT YOU TYPED IN YOUR CALCULATOR!
5. At the Airtight Security Company, every employee must wear a badge with an identification code consisting of 2 letters of the 26 letters a – Z, followed by 2 of the digits 0 – 9. Letters and digits may be
repeated, but the first letter CANNOT be the letter O. How many different codes can be made?
SHOW WHAT YOU TYPED IN YOUR CALCULATOR!
6. A bag contains 5 red jelly beans, 4 green jelly beans, and 3 white jelly beans. If a jelly bean is selected
at random from the bag, what is the probability that you pull out a green jelly bean and then a white jelly
bean without replacing the first one? SHOW WORK AND LEAVE YOUR ANSWER AS A
REDUCED FRACTION!
7. You roll a number cube labeled 1 – 6 and toss a fair coin. What is the probability that you will roll an
even number and the coin will land on tails? SHOW WORK AND LEAVE YOUR ANSWER AS A
REDUCED FRACTION!
8. The following chart shows the current enrollment in all the mathematics classes offered by Eastside
High School. What is the average number of students enrolled per section in Algebra 1? SHOW WORK!
Course Title
Pre-Algebra
Algebra 1
Geometry
Algebra II
Pre-Calculus
Section
A
A
B
C
A
B
A
A
Period
3
2
3
4
1
2
4
6
Enrollment
23
24
25
29
21
22
28
19
WORK:
9. You work for a car manufacturer. You can choose from three different body styles, manual or
automatic transmission, and five different paint colors. How many different cars could a customer create?
SHOW WHAT YOU TYPED IN YOUR CALCULATOR!
10. You are pet-sitting for two dogs. One dog must be fed every six hours, and the other dog must be fed
every eight hours. You just fed both dogs at the same time. How many hours will pass before you will
feed them both at the same time?
A.
B.
C.
D.
E.
2
6
8
24
48
11. So far, a student has earned the following scores on four 100-point tests this grading period: 65, 73,
81, and 82. What score must the student earn on the fifth and last 100-point test of the grading period to
earn an average test grade of 80 for the 5 tests? SHOW WORK!
12. There are three students that are giving speeches at graduation. How many different orders can be
created? SHOW WHAT YOU TYPED IN YOUR CALCULATOR!
13. The average height of 4 buildings is 20 meters. If 3 of the buildings are each 16 meters tall, what is
the height, in meters, of the fourth building? SHOW WORK!
14. If the average of your first five test scores is 89, what do you need to get on the sixth test to bring
your average up to a 90? SHOW WORK!
15. Create a test question similar involving the topics covered in this section. Show work for the correct
answer. Explain why your answer choices are “tricky”.
Question:
A.
B.
C.
D.
E.
Name ________________________________
Probability, Averages, and Counting Techniques PRACTICE B
1. A bag contains 5 red jelly beans, 4 green jelly beans, and 3 white jelly beans. If a jelly bean is selected
at random from the bag, what is the probability that the jelly bean selected is green?
2. Find the mean of the following values: 43, 17, 24, 35, and 41?
WORK:
3. So far, a student has earned the following scores on four 100-point tests this grading period: 65, 73, 81,
and 82. What score must the student earn on the fifth and last 100-point test of the grading period to earn
an average test grade of 80 for the 5 tests?
F. 75
G. 76
H. 78
J. 99
K. The student cannot earn an average of 80.
4. What is the least common multiple of 80, 70, and 90?
A. 80
B. 240
C. 504
J. 5,040
K. 504, 000
5. To create a password, you must use three of the 26 alphabet letters (A – Z), followed by one of the 10
numeric digits (0 – 9). How many different passwords can be created? NOTE: letters MAY be repeated.
SHOW WHAT YOU TYPED IN YOUR CALCULATOR!
____ X _____ X _____ X ______ =
6. If a marble is randomly chosen from a bag that contains exactly 8 red marbles, 6 blue marbles, and 6
white marbles, what is the probability that the marble will NOT be white?
3
4
3
G.
5
4
H.
5
3
J.
10
7
K.
10
F.
7. Kareem has 4 sweaters, 6 shirts, and 3 pairs of slacks. How many distinct outfits, each consisting of a
sweater, a shirt, and a pair of slacks, can Kareem select? SHOW WHAT YOU TYPED IN YOUR
CALCULATOR!
____ X ____ X ____ =
8. You roll a number cube labeled 1 – 6 and toss a fair coin. What is the probability that you will roll a 2
on the cube and the coin will land on tails? SHOW WORK AND LEAVE YOUR ANSWER AS A
REDUCED FRACTION!
9. If you flip a coin three times, what is the probability that it will land on heads all three times?
A. 1/2
B. 1/4
C. 3/2
D. 1/8
E. It cannot land on heads all three times
10. You are pet-sitting for two dogs. One dog must be fed every three hours, and the other dog must be
fed every six hours. You just fed both dogs at the same time. How many hours will pass before you will
feed them both at the same time?
A.
B.
C.
D.
E.
3
6
9
18
Cannot be determined with the given information
11. The average of Bob’s 3 test scores was 80. If the average of his first two tests was also 80, what is his
score on the third test? SHOW WORK!
F. 90
G. 85
H. 80
J. 75
K. 72
12. The student council has 30 members. They have to choose a President, a Vice-President, a Secretary,
and a Treasurer. If each person can hold only one office, which calculation shows the number of ways
these officers can be selected?
A.
B.
C.
D.
E.
30 4
30 4
30  29  28  27
30  29  28  27
30  30  30  30
13. Two traffic lights are on timers. The first light will change every 30 seconds, and the second light
changes every 45 seconds. They both just changed at the same time. How many seconds will pass before
they change at the same time again?
F. 5 seconds
G. 15 seconds
H. 30 seconds
J. 90 seconds
K. 1350 seconds
14. The average of seven test scores is 68. If an eighth test is taken, what is the minimum score needed
in order to bring up the average to a 70? SHOW WORK!
A. 9.7
B. 59.5
C. 69
D. 84
E. The average cannot be brought up to a 70 with just one more test.
15. Create a test question similar involving the topics covered in this section. Show work for the correct
answer. Explain why your answer choices are “tricky”.
Question:
A.
B.
C.
D.
E.