Here is the sample space for rolling a number cube and flipping a coin: 1H, 1T, 2H, 2T, 3H, 3T, 4H, 4T, 5H, 5T, 6H, 6T Where 1-6 represents the possible outcomes of rolling the number cube and H and T represent the outcomes of flipping the coin (Heads or Tails). This gives a total of 12 possible outcomes using a list to represent the sample space.

1. A number cube is tossed 24 times and lands on 1 three times and on 2
four times.
1. Find the experimental probability of landing on 1.
2. Find the theoretical probability of not landing on 1.
3. Find the theoretical probability of landing on 2.
4. Find the experimental probability of not landing on 2.
5. State the difference between theoretical and experimental
probabilities.
6. In one afternoon, 24 restaurant customers order steak, 18 order
sandwiches, and 20 order salads. Based on these orders, what is
the probability that the next customer will order a salad?
Course 2, Lesson 9-3

2. Course 2, Lesson 9-3
ANSWERS
1. 2.
3. 4.
5. An experimental probability is based on information gained by an
experiment or game, while a theoretical probability is based on a
ratio of favorable outcomes to possible outcomes.
6.
1
8
5
6
1
6
5
6
10
31

3. HOW can you predict
the outcome of future events?
Statistics and Probability
Course 2, Lesson 9-3

4. Statistics and Probability
• 7.SP.8
Find probabilities of compound events using organized lists, tables,
tree diagrams, and simulation.
• 7.SP.8a
Understand that, just as with simple events, the probability of a
compound event is the fraction of outcomes in the sample space for
which the compound event occurs.
• 7.SP.8b
Represent sample spaces for compound events using methods such
as organized lists, tables and tree diagrams. For an event described
in everyday language (e.g., “rolling double sixes”), identify the
outcomes in the sample space which compose the event.
Course 2, Lesson 9-3 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices
and Council of Chief State School Officers. All rights reserved.

5. Course 2, Lesson 9-3 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council
of Chief State School Officers. All rights reserved.
Statistics and Probability
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
5 Use appropriate tools strategically.

6. • To find a sample space
• To find probability
Course 2, Lesson 9-3
Statistics and Probability

7. Course 2, Lesson 9-3
Statistics and Probability
• sample space
• tree diagram
• compound event

8. 1
Need Another Example?
2
3
Step-by-Step Example
1. The three students chosen to represent
Mr. Balderick’s class in a school assembly
are shown. All three of them need to sit in
a row on the stage. Use a list to find the
sample space for the different ways they
can sit in a row.
Use A for Adrienne, C for Carlos, and G for Greg.
So, the sample space consists of 6 outcomes.
Use each letter exactly once.
ACG AGC CAG CGA GAC GCA

9. Answer
Need Another Example?
Melinda has four pictures that she wants to
place in a column in her scrapbook. Use a list
to find the sample space for the different
ways she can place the pictures.
1234, 1243,1324, 1342, 1423, 1432, 2134,
2143, 2314, 2341, 2413, 2431, 3124, 3142,
3214, 3241, 3412, 3421, 4123, 4132, 4213,
4231, 4312, 4321

10. 1
Need Another Example?
2
Step-by-Step Example
A car can be purchased in blue, silver, red, or purple. It also comes as a
convertible or hardtop. Use a table or a tree diagram to find the sample
space for the different styles in which the car can be purchased.
Using either method, the sample space consists of 8 outcomes.
2.
Color Top
Sample
Space
Blue
Convertible
Hardtop
BC
BH
Silver
Convertible
Hardtop
SC
SH
Red
Convertible
Hardtop
RC
RH
Purple
Convertible
Hardtop
PC
PH

11. Answer
Need Another Example?
An Italian ice shop sells lime, cherry, blueberry, and watermelon
Italian ice. You can get it served plain, mixed with ice cream, or
as a drink. Use a table or tree diagram to find the sample space
for the different orders that can be made.
LP, LI, LD, CP, CI, CD, BP, BI, BD, WP, WI, WD

12. 1
Need Another Example?
2
3
Step-by-Step Example
Suppose you toss a quarter, a dime, and a nickel. Find the sample space.
What is the probability of getting three tails?
P(3 tails) =
3.
Make a tree diagram to show the sample space.
Quarter Dime Nickel Sample Space
heads
tails
heads
tails
heads
tails
heads
tails
heads
tails
heads
tails
heads
tails
heads, heads, heads
heads, heads, tails
heads, tails, heads
heads, tails, tails
tails, heads, heads
tails, heads, tails
tails, tails, heads
tails, tails, tails
So, the probability of getting three tails is .

13. Answer
Need Another Example?
The school cafeteria gives students two choices of
snacks: carrot sticks and pretzels. They also offer a
beverage choice of apple juice, low-fat milk, or bottled
water. Find the sample space for all possible orders of
one snack with one beverage. What is the probability
of someone getting pretzels and apple juice?
Snack
carrot
sticks (C)
pretzels (P)
Beverage
apple juice (A)
lowfat milk (M)
bottled water (W)
apple juice (A)
lowfat milk (M)
bottled water (W)
Sample
Space
(CA)
(CM)
(CW)
PA
PM
PW

14. 1
Need Another Example?
2
Step-by-Step Example
To win a carnival prize, you
need to choose one of 3
doors labeled 1 through 3.
Then you need to choose a
red, yellow, or blue box
behind each door. What is the
probability that the prize is in
the blue or yellow box behind
door 2?
4.
The table shows that there are 9 total
outcomes. Two of the outcomes are favorable.
So, the probability that the prize is
in a blue or yellow box behind door 2 is .

15. Answer
Need Another Example?
A cell phone company is offering a special deal. If you choose from
payment plans A, B, and C and one of four different phones, you can
choose a free gift of a case, a car charger, or a memory card. What is
the probability that Jamal will choose plan A, phone 2, and the car
charger?

16. How did what you learned
today help you answer the
Course 2, Lesson 9-3
GeometryStatistics and Probability
HOW can you predict
the outcome of future events?

17. How did what you learned
today help you answer the
Course 2, Lesson 9-3
GeometryStatistics and Probability
HOW can you predict
the outcome of future events?
Sample answers:
• By finding a sample space of possible outcomes
• By using an organized list, a table, or a tree diagram to
find a sample space
• By finding the probability of a compound event

18. Use any method to give
the sample space for
rolling a number cube
and flipping a coin.
Course 2, Lesson 9-3
Ratios and Proportional RelationshipsFunctionsStatistics and Probability