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Objective
Use tree diagrams to count outcomes and
find probabilities
Vocabulary
Fair game
A game in which players of equal skill have an
equal chance of winning
Vocabulary
Tree diagram
A diagram used to show the total number of
possible outcomes in a probability experiment
Vocabulary
Sample space
The set of all possible outcomes of a probability
experiment
Example 1 Draw a Tree Diagram
Example 2 Find the Number of Outcomes
Example 3 Find Probability Using Tree Diagrams
CHILDREN 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.
There are 4 possible
outcomes
Outcome
Outcome
There is only 1 possible
chance of having 2 girls
Answer: P(2 girls) =
1/3
COINS A game involves flipping two pennies. Draw a
tree diagram to show the sample space of the results
in terms of heads and tails. Then determine the
probability of flipping one head and one tail.
Answer: P(one head, one tail) =
1/3
ICE CREAM 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. For toppings, you
can have hot fudge, butterscotch, or marshmallow.
Find the number of different sundaes that are
possible.
Make a tree diagram to show the sample space.
Make 3 columns:
Ice Cream
Topping
Outcome
2/3
Identify ice cream types
Answer: There are 9 different sundaes possible.
2/3
CARS A new car can be ordered with exterior color
choices of black, blue, red, and white, and interior
color choices of tan, gray, and blue. Find the number
of different cars that are possible.
Answer: 12 different cars possible
2/3
ICE CREAM 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. For toppings, you can
have hot fudge, butterscotch, or marshmallow. If you are
given a sundae at random from the Ice Cream Shoppe,
cream
what is the probability that it has vanilla ice cream?
Use the tree diagram made in Example 2 to help find the
probability
Write probability statement
P (vanilla ice cream) = Number with vanilla ice cream
Total number of sundaes
3/3
P (vanilla ice cream) =
Number with vanilla ice cream
Total number of sundaes
P (vanilla ice cream) =
3
9
3/3
P (vanilla ice cream) =
Number with vanilla ice cream
Total number of sundaes
3 3
P (vanilla ice cream) = 9  3
Answer:
1
P (vanilla ice cream) =
3
Find the GCF = 3
Divide GCF into numerator
and denominator
3/3
*
CARS A new car can be ordered with exterior color
choices of black, blue, red, and white, and interior
color choices of tan, gray, and blue. If you select a car
at random, what is the probability that the exterior
color is blue?
Answer: P(blue) =
3/3
Assignment
Lesson 9:2
Tree Diagrams
7 - 14 All