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Lesson 9-2 Pages 374-377
Tree Diagrams
Lesson Check 9-1
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What you will learn!
How to use tree diagrams to count outcomes and
find probabilities.
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Fair gameFair gameTree diagramTree diagramSample spaceSample space
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What you really need to know!
A game in which players of equal skill have an equal chance of winning is a fair game. A tree diagram is used to show all of the possible outcomes, or sample space, in a probability experiment.
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Link to Pre-Made Lesson
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Example 1:
Tom flips two coins. Draw a tree diagram to show the sample space of how the coins can land. Then determine the probability of flipping two tails.
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First First CoinCoin
H
T
H
T
T
H
HH
HT
TH
TT
Second Second CoinCoin
Sample Sample SpaceSpace
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The probability of flipping two tails is:
possible
favorableP(tails)
4
1
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Choices x Choices = Number of outcomes
2 x 2 = 4 possibilities
Example 1: Method 2
4
1
possible
favorableP(tails)
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Example 2:
An ice cream sundae at the Ice Cream Shoppe is made from one flavor of ice cream and one topping. For ice cream flavors, you can choose from chocolate, vanilla, and strawberry.
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Example 2:
For toppings you can have hot fudge, butterscotch, or marshmallow. Find the number of different sundaes that are possible.
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Ice CreamIce Cream
9 possibilities!C
V
S
F
B
M
F
B
M
F
B
M SM
CF
CB
CM
VF
VB
VMSF
SB
ToppingTopping Sample SpaceSample Space
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Choices x Choices = Number of outcomes
3 x 3 = 9 possibilities
Example 2: Method 2
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Example 3:
If you are given a sundae at random from the shop in the previous problem, what is the probability that it has vanilla ice cream?
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Ice CreamIce Cream ToppingTopping Sample SpaceSample Space
9 possibilities!C
V
S
F
B
M
F
B
M
F
B
M SM
CF
CB
CM
VF
VB
VMSF
SB
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Example 3:
If you are given a sundae at random from the shop in the previous problem, what is the probability that it has vanilla ice cream?
possible
favorableP(vanilla)
3
1
9
3
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Page 376
Guided Practice
#’s 3-6
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Pages 374-375 with someone at home and study
examples!
Read:
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Homework: Page 376-377
#’s 7-19 all
#’s 23-33
Lesson Check 9-2THQ 9-1/9-2 Tree Diagrams
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Page
585
Lesson 9-2
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Lesson Check 9-2
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Example 1:
A family has two children. Draw a tree diagram to show the sample space of the children’s genders. Then determine the probability of the family having two girls.
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First First ChildChild
Second Second ChildChild
Sample Sample SpaceSpace
B
G
B
G
BB
BG
GB
GG
B
G
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The probability of having two girls is:
possible
favorableP(girls)
4
1
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THQ 9-1 to 9-2
Tree Diagrams
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YRBG
R
B
G
Y
B
G
Y
R
G
Y
R
B
B
G
R
G
R
B
B
G
Y
G
Y
B
R
G
Y
G
Y
R
R
B
Y
B
Y
R
G
B
G
R
B
R
G
B
G
Y
B
Y
G
R
G
Y
R
Y
B
R
B
Y
R
Y
YRBG
YRGB
YBRG
YBGR
YGRB
YGBR
RYBG
RYGB
RBYG
RBGY
RGYB
RGBY
BYRG
BYGR
BRYG
BRGY
BGYR
BGRY
GYRB
GYBR
GRYB
GRBY
GBYR
GBRY
# 4
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RB
CAR1CAR1
CAR2CAR2
CAR3CAR3
CAR4CAR4
CAR1CAR1
CAR2CAR2
CAR3CAR3
CAR4CAR4
R CAR1R CAR1
R CAR2R CAR2
R CAR3R CAR3
R CAR4R CAR4
B CAR1B CAR1
B CAR2B CAR2
B CAR3B CAR3
B CAR4B CAR4
# 5