(7) Lesson 9.5

1. Use the act it out strategy to solve Exercises 1–4.
1. Four friends all shake hands with one another. How many
handshakes take place?
2. Liz needs to clean her room, walk the dog, and do her homework. In
how many ways can she do these three things?
3. Five friends ran a race. In how many possible ways could the friends
have finished the race?
4. Diego, Caroline, Blythe, and Andrew are a team playing tug-of-war.
In how many different ways can they be arranged?
5. Three students are to be chosen from auditions of 9 students to play
lead roles in the school play. In how many ways can these three
students be chosen?
Course 2, Lesson 9-5

2. Course 2, Lesson 9-5
ANSWERS
1. 24
2. 6
3. 120
4. 24
5. 504

3. HOW can you predict
the outcome of future events?
Statistics and Probability
Course 2, Lesson 9-5

4. Course 2, Lesson 9-5 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
• 7.SP.5
Understand that the probability of a chance event is a number
between 0 and 1 that expresses the likelihood of the event
occurring. Larger numbers indicate greater likelihood. A probability
near 0 indicates an unlikely event, a probability around 1/2 indicates
an event that is neither unlikely nor likely, and a probability near 1
indicates a likely event.
• 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.

5. Course 2, Lesson 9-5 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
• 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.
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.

6. • To use the Fundamental Counting
Principle to find the number of
possible outcomes in a sample
space
• To use the Fundamental Counting
Principle to help find probability
Course 2, Lesson 9-5
Statistics and Probability

7. Course 2, Lesson 9-5
Statistics and Probability
• Fundamental Counting Principle

8. Course 2, Lesson 9-5
Statistics and Probability
If event M has m possible outcomes, and event N has n
possible outcomes, then event M followed by event N has
m x n possible outcomes.

9. 1
Need Another Example?
2
3
Step-by-Step Example
Find the total number of outcomes when a coin is tossed and a
number cube is rolled.
1.
A coin has 2 possible outcomes. A number cube has 6 possible outcomes.
Multiply the possible outcomes of each event.
There are 12 different outcomes.
Check
2
Fundamental
Counting Principle● 6 = 12
Coin Number Cube Sample Space
heads
1
2
3
4
5
6
heads, 1
heads, 2
heads, 3
heads, 4
heads, 5
heads, 6
Draw a tree diagram to show the sample space.
4 The tree diagram also shows that there are 12 outcomes.
Coin Number Cube Sample Space
tails
1
2
3
4
5
6
tails, 1
tails, 2
tails, 3
tails, 4
tails, 5
tails, 6

10. Answer
Need Another Example?
Find the total number of outcomes when a number
from 0 to 9 is picked randomly, and then when a
letter from A to D is picked randomly.
40

11. 1
Need Another Example?
2
3
Step-by-Step Example
Find the total number of outcomes from rolling a number cube with
sides labeled 1-6 and choosing a letter from the word NUMBERS.
Then find the probability of rolling a 6 and choosing an M.
2.
There are 42 different outcomes.
There is only one favorable outcome. So, the probability
of rolling a 6 and choosing an M is or about 2%.
6
Fundamental
Counting Principle● 7 = 42

12. Answer
Need Another Example?
A pizzeria has two different types of crust, 3 types of
cheese, and 4 toppings. A personal pizza can only
have one type of cheese and one topping. What is
the probability of choosing a thin crust pizza with
parmesan cheese and pepperoni?

13. 1
Need Another Example?
2
3
Step-by-Step Example
Find the number of different jeans available at The Jeans Shop.
Then find the probability of randomly selecting a size 32 × 34 slim
fit. Is it likely or unlikely that the jeans would be chosen?
3.
There are 45 different types of jeans to choose. Out of the 45 possible
outcomes, only one is favorable. So, the probability of randomly selecting
a 32 × 34 slim fit is or about 2%.
It is very unlikely that the size would be chosen at random.
3
Fundamental
Counting Principle●5 = 45● 3

14. Answer
Need Another Example?
A shoe store sells sneakers, loafers, and boots in
narrow, medium, and wide widths. They are available
in sizes 6, 6.5, 7, 7.5, 8, 8.5, 9, 9.5, 10, and 10.5.
Find the number of pairs of shoes available. Then find
the probability of selecting a size 8 in medium width
sneakers. Is it likely or unlikely that the size would be
chosen?
90, , 1.1%; It is very unlikely that
the size would be chosen at random.

15. 1
Need Another Example?
2
3
4
Step-by-Step Example
A box of toy cars contains blue, orange, yellow, red, and black cars.
A separate box contains a male and a female action figure. What is
the probability of randomly choosing an orange car and a female
action figure? Is it likely or unlikely that this combination is chosen?
4.
First, find the number of possible outcomes.
There are 10 possible outcomes. There is one way to
choose an orange car and a female action figure. It is
very unlikely that this combination is chosen at random.
There are 5 choices for the car and 2 choices for the action figure.
Fundamental Counting Principal
P(orange car, female action figure) = or 10%.
5 • 2 = 10

16. Answer
Need Another Example?
The two spinners below are spun. What is the
probability that the product of the numbers spun is
12? How likely is it that the product would be 12?
or 4%; very unlikely

17. How did what you learned
today help you answer the
Course 2, Lesson 9-5
GeometryStatistics and Probability
HOW can you predict
the outcome of future events?

18. How did what you learned
today help you answer the
Course 2, Lesson 9-5
GeometryStatistics and Probability
HOW can you predict
the outcome of future events?
Sample answers:
• By using the Fundamental Counting Principle to find a
sample space
• By using the Fundamental Counting Principle to find
the probability of an event

19. Suppose you have 4 kinds of cereal
(A, B, C, and D) and two kinds of
berries (strawberries and blueberries)
to put on the cereal. Describe the
method you would use to find
the sample space. Then find the
probability of having cereal A
with strawberries.
Course 2, Lesson 9-5
Ratios and Proportional RelationshipsFunctionsStatistics and Probability