Pre-Algebra
Tree Diagrams
1
What Are You Learning?
•I CAN use tree
diagrams to find
sample space.
2
Why Do You Need To Know This?
• Tree diagrams are useful because they
give another way to find the sample space
of various real world events.
• They are also useful in finding the
probabilities of various events.
3
Vocabulary
• Fair game—game in which players of equal skill
have an equal chance of winning.
• Tree diagram—used to show the total number
of possible outcomes in a probability
experiment.
• Sample space—the set of all possible outcomes
of a probability experiment.
4
• A school team sells caps in two colors
(blue or white), two sizes (child or adult),
and two fabrics (cotton or polyester).
• Draw a tree diagram to find the # of cap
choices.
5
The 7th grade class sells cold
drinks.
• Customers can choose
small, medium, or large.
• There are 5 drinks: cola,
diet cola, root beer,
lemonade, and water.
• Customers may choose
ice or no ice.
a. Find the total # of
possible outcomes.
b. What is the
theoretical probability
that a customer will
order a medium diet
cola with no ice?
6
Use a tree diagram to find the
sample space for tossing two coins.
a.Find P(2 tails).
b.Find P(one head and
one tail.)
7
Scooters
• A certain type of scooter comes in silver,
red, or purple with wheel sizes of 125 mm
or 180 mm.
• Find the total # of color-wheel
combination.
8
Children
• A family has two children. Draw a tree
diagram to show the sample space of the
children’s gender.
• Find P(2 girls)
• Find P(boy and girl)
9
Suppose Pablo tosses three pennies.
a. Find his sample space.
b. Find P(3 heads)
c. Find P(3 tails)
d. Find P(exactly 2 heads)
e. Find P(at least 1 tail)
10
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 # of
different
sundaes that
are possible.
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Make a tree diagram for each situation.
Show the sample space and give the total # of outcomes.
a.
choosing a letter from
the word SPACE and
choosing a consonant
from the word MATH
b.
choosing black, blue, or
brown socks with boots,
gym shoes, or dress
shoes
c.
picking a # from 1 to 5
and choosing a color
red, white, or blue
d.tossing a coin and
rolling an # cube
e.choosing a purple,
green, black ,or
silver mountain
bike having 10, 18,
21, or 24 speeds
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Class Work
• Practice Skills and Word Problems 9-2
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