Name: _______________________
Probability – Sample Space and The Counting Principle
Date: _______
Class: Pre-Algebra
Sheet # 09-03
Example Problem:
Mr. Krabs has made a new menu for the Krusty Krab restaurant. He’s asked SpongeBob to make a
sign to advertise the new menu. SpongeBob is really excited but he needs some help. Customers
can make a meal by picking one patty, one side and one drink. The items are listed below.
PATTY
SIDES
DRINK
 Original Krabby Patty
 Coral Bits
 Kelp Shake
 Veggie Krabby Patty
 Barnacle Bites
 Kelp Cola
 Krabby Patty with Jellyfish Jelly
 Kelp Juice
Part A
SpongeBob wants to advertise how many value meals can
be made by picking one patty, one side and one drink.
Help fill in the blank in SpongeBob’s sign.
1
2
List the sample space of tossing a coin twice.
List the sample space of choosing a letter from the
word SPACE and choosing a consonant from the
word COW.
Part B What method did you use for Part A?
Answer _____________________
Part C
SpongeBob wants to make a list of all the possible value
meals a customer can make by choosing one patty, one
side, and one drink. What method can he use?
3
Answer _____________________
A coin is tossed and the spinner to
the right is spun.
Create a tree diagram to display the
sample space of the event.
Part D
Use the method you stated in Part C to help SpongeBob
find all the possible value meals.
4
ERROR ANALYSIS
Vinny wants to determine the probability of guessing
correctly on two true-false questions on his history
test. He draws the tree diagram below using C for
correct and I for incorrect. Find his mistake and
correct it.
5
During an experiment, the two spinners below
will be spun.
7
For the lunch special at Nico’s Deli, customers
can create their own sandwich by selecting 1 type
of bread and 1 type of meat from the selection
below
Represent the sample space for this experiment.
.
In the space below, list all the possible sandwich
combinations using 1 type of bread and 1 type of meat.
Use the Fundamental Counting Principle to check your
sample space.
How many of these outcomes consist of a green and an A?
If Nico decided to add whole wheat bread as another bread
option, how many possible sandwich combinations will
there be?
Answer __________
6
Answer _________sandwich combinations
Frank is picking out his lunch from
the cafeteria menu below.
8
Sandwich
Cookie
Drink
Grilled Cheese (G)
Peanut Butter Jelly (P)
Tuna (T)
Oreo (O)
Chocolate Chip (C)
Milk (M)
Juice (J)
During an experiment, three coins were tossed
once.
Part A Give the sample space to show all possible
outcomes for tossing three coins one time, using the letter
H when a coin faces “heads” up, and the letter T when it
faces “tails” up.
Part A Make a tree diagram of all possible lunches Frank
can create by choosing one sandwich, one cookie and one
drink.
Part B Based on your answer to part A, how many
outcomes consist of 3 heads or 3 tails?
Part B Use the Fundamental Counting Principle to check
your sample space.
Part C Find the probability that Frank creates a lunch with
grilled cheese OR an Oreo.
Answer __________
Part C During a math class, each of 24 students tossed
three coins once. Based on your answer to part B, how
many students would you expect to get a result of 3 heads
or 3 tails?
Answer __________
Part D Find the probability that Frank creates a lunch with
grilled cheese AND an Oreo.
Answer __________
Answer __________
Name: _______________________
Probability – Sample Space and The Counting Principle
1
A school is voting on a new mascot. The choices
for the type and style are listed in the table below.
Date: _______
Class: Pre-Algebra
5
Make a tree diagram of all the possible school mascots
using one type and one style.
Sheet # 09-04
Mr. Nocella loves to clown around on the weekends!
Each Saturday night he picks out a clown suit, he
puts on a wig and then he chooses one of his talents
to entertain all his friends.
His choices are listed
in the table. Use the
Fundamental
Counting Principle to
find the total number
of possible ways Mr.
Nocella enters clown
town.
List the sample space.
6
Use the Fundamental Counting Principle to check your
sample space.
2
Your school combination lock is
numbered from 0 to 39. Each
combination uses three numbers in
a right, left, right pattern. Find the
total number of possible
combinations for the lock.
Mrs. Schoen is purchasing a new car. She has the
choice of either a 2-door or a 4-door, an automatic
or a manual, and the color of red, blue or black. Use
the Fundamental Counting Principle to determine
the number of outcomes.
Answer ______________
7
A shipping company uses baggage tags with 3letter city codes. The first and third letters of
each code are always consonants and middle
letter is always a vowel. The English language
uses 21 consonants and 5 vowels. How many
different combinations of tag codes are possible?
Answer ______________
3
Use the Fundamental Counting Principle to find
the total number of possible outcomes.
8
4
Use the Fundamental Counting Principle to find
the total number of possible outcomes.
A
105
C
1,638
B
441
D
2,205
Grace stands in the lunch line at school. For her
meal, she can choose spaghetti or pizza. She can
also have apple juice, orange juice, or milk. How
many different combinations of one meal and one
drink can Grace choose?
A
2
C
5
B
3
D
6
9
Noelle draws a marble from the pile below and
then flips a penny. How many possible
combinations of marbles and flips are there?
14
How many different combinations are there for
picking a month of the year and a day of the
week?
Answer: ______________
15
10
11
A
6
C
12
B
10
D
16
A student tosses the coin and rolls the number
cube. How many outcomes are possible in this
situation?
A
2
C
8
B
6
D
12
A sandwich shop offers 4 different meats and 2
different cheeses. Suppose the sandwich shop
offers 24 different meat-cheese sandwiches.
How many different breads does the sandwich
shop use?
Answer: ______________
16
Pam wants to buy a suitcase. The order form she
uses is shown below.
How many different combinations of color, size, and
material are possible for Pam’s suitcase?
Riley has 4 blouses, 6 skirts and 10 hair bows.
Part A Find the number of different outfits that Riley can
wear if she chooses 1 blouse, 1 skirt and 1 hair bow.
17
Answer: __________ outfits
Part B
Riley has 1 favorite blouse/skirt/bow combo. What is the
probability that she randomly puts together that outfit?
A
10
C
24
B
15
D
30
JUSTIFY CONCLUSIONS
A store offers 32 different t-shirt designs and 11
choices of color. Is the stores advertisement true?
Explain.
Answer: ______________
Part C
Is the probability of the event in Part B likely or unlikely?
Answer: ______________
12
How many different combinations are there for
answers to a 5 question True-False quiz?
18
[By the way, it is VERY RARE that anyone gets this
correct the first time. List the sample space to check
yourself.]
Answer: ______________
13
How many different outcomes are there for
tossing a quarter, dime, and nickel?
Answer: ______________
19
PERSEVERE WITH PROBLEMS
Determine the number of possible outcomes when
tossing one coin, two coins, and three coins. Then
determine the number of possible outcomes for
tossing n coins. Describe the strategy you used.
Compare and contrast tree diagrams and the
Fundamental Counting Principle.