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Lesson 8-4
Objective - To represent the sample space of a
compound event using tables or tree diagrams.
List the sample space for flipping a coin and rolling
an even number on a die.
Tree Diagram
Table
Coin Die Outcomes
Die
2
H2
2 4 6
4
H
H4
6
H6
Coin H H2 H4 H6
T2
T T2 T4 T6
2
T4
4
T
T6
H2, H4, H6, T2, T4, T6
6
- Good for 2+ events,
few outcomes
- Good for 2 events,
many outcomes
Probability of Multiple Events - Tree Diagrams
A nickel, dime, and quarter are tossed. Find the
probability of the following.
Nickel
Dime
H
H
T
H
T
T
1) P(Only one heads)
3
8
Quarter Outcomes
H
T
H
T
H
T
H
T
HHH
HHT
HTH
HTT
THH
THT
TTH
TTT
←
←
←
←
2) P(At least two heads)
4
1
= 2
8
Multiplication Counting Principle
(Fundamental Counting Principle)
The total outcomes for a compound event equals
the product of all the outcomes for each single event.
How many outcomes are possible when flipping the
coin rolling the die
coin,
die, and spinning the spinner?
7
6
Outcomes:
2
6
8 1
5 4
8
Total Outcomes: 2 × 6 × 8 = 96 ways
Probability of Multiple Events - Tree Diagrams
A nickel, dime, and quarter are tossed. Find the
probability of the following.
Nickel
Dime
Quarter Outcomes
H
T
H
T
H
T
H
T
H
H
T
H
T
T
1) P(Only one heads)
3
8
HHH
HHT
HTH
HTT
THH
THT
TTH
TTT
←
←
←
2) P(At least two heads)
Probability of Multiple Events - Table
Find the probability of rolling a sum of 7 with
two six-sided die.
Event 1 - First Die
1 2 3 4 5 6
1
2
Event 2 3
Second
4
Die
5
6
2
3
4
5
6
7
3
4
5
6
7
8
4
5
6
7
8
9
5
6
7
8
9
10
6 7
7 8
8 9
9 10
10 11
11 12
Sum of
the dice
1
P(sum of 7) = 6 =
6
36
Counting Possibilities
Jefferson Middle School’s dress code allows students
to pick from a green, blue or white shirt and black
or blue jeans. Use a table to count the possibilities.
Blue Shirt
White Shirt
Green Shirt
Black Jeans
Blue Shirt
Black Jeans
White Shirt
Black Jeans
Green Shirt
Black Jeans
Blue Jeans
Blue Shirt
Blue Jeans
White Shirt
Blue Jeans
Green Shirt
Blue Jeans
2
3
3 × 2 = 6 outcomes
Math 6 Slide Show: Teaching Made Easy As Pi, by Mike Mills and James Wenk © 2011
Lesson 8-4 (cont.)
1) If you have four shirts, six pairs of pants and
eight pairs of socks. How many different outfits can
you wear?
4 × 6 × 8 = 192 outfits
3) Multiplication Counting Principle
How many ways are there for Terry to leave home,
go to the store, go to the bank, and then home again?
Home
2) If you have three meats, five cheeses, and four
types of bread. How many different sandwiches
can you make?
3 × 5 × 4 = 60 sandwiches
4 ways
Store
2 ways
3 ways
Bank
Number of ways to do them all = 4 • 3 • 2 = 24 ways
4) Multiplication Counting Principle
How many different 3 digit area codes are possible?
Find the total number of outcomes for each compound
event and state which representation would best display
the outcomes, table or tree diagram.
1) Flipping 4 coins at once.
Total outcomes = 2 • 2 • 2 • 2 = 16
# of
possible = 10
digits
10
10 = 1000 ways
Tree Diagram
2) Drawing a marble from the bag twice.
Total outcomes = 5 • 5 = 25
Table
R
P
B
G
Find the total number of outcomes for each compound
event and state which representation would best display
the outcomes, table or tree diagram.
3) Spinning the spinner twice.
Total outcomes = 3 • 3 = 9
Tree Diagram or Table
4) Rolling a die 3 times.
Total outcomes = 6 • 6 • 6 = 216
Tree Diagram
1
3
2
W
Find the total number of outcomes for each compound
event and state which representation would best display
the outcomes, table or tree diagram.
5) Making snacks with crackers (Round, Salt,
wheat, 7-Grain) and cheese (cheddar, Swiss, brie,
muenster, and blue cheese).
Total outcomes = 4 • 5 = 20
Table
Math 6 Slide Show: Teaching Made Easy As Pi, by Mike Mills and James Wenk © 2011
Lesson 8-4 (cont.)
Find the total number of outcomes for each compound
event and state which representation would best display
the outcomes, table or tree diagram.
6) Making a smoothie with one ingredient from
each category.
Base
Fruit
Fortify
Protein
Banana
Milk
Vitamin
Strawberry
Yogurt
Pineapple
Ice Cream
Berry
Total outcomes = 3 • 4 • 2 = 24 ways
Tree Diagram
Math 6 Slide Show: Teaching Made Easy As Pi, by Mike Mills and James Wenk © 2011