Probability: Visual Representations

Unit 8: Probabilistic Reasoning

Lesson 4: Determining Probability Using Visual Representations

Learning Standards

NC.7.SP.8 Determine probabilities of compound events using
organized lists, tables, tree diagrams, and simulation.

b. For an event described in everyday language, identify the
outcomes in the sample space which compose the event, when the
sample space is represented using organized lists, tables, and tree
diagrams.

Learning Targets

●I can define sample space.

●I can use a visual aid to list sample spaces of a probability pool.

●I can use a visual aid to determine probabilities of compound events.

Defining Sample Space

A sample space
describes the
possible outcomes
of a probability pool.
It tells you what the
outcomes are in
addition to how
many outcomes
there are.

Examples:

The sample space for a fair coin flip:

S = {heads, tails}

The sample space for a fair number number cube:

S = {1, 2, 3, 4, 5, 6}

The sample space for this spinner:

S = {yellow, green, yellow, blue, yellow, orange}

*Pick one example to copy down

Defining Sample Space

Sample spaces
can be
represented
with lists (as
they were on the
previous slide)
and tables (as
they are on this
slide).

Sample space for
fair coin:

H

T

Sample space for fair,
standard number cube:

1

2

3

4

5

6

Sample space for spinner:

yellow

green

yellow

blue

yellow

orange

Multiple Choice

Simon is having cereal for breakfast and has the five choices pictured. What is the sample space of choices?

• Honey Nut Cheerios

• Cinnamon Toast Crunch, Honey Nut Cheerios and Reese's Puffs

• Cinnamon Toast Crunch, Cocoa Puffs, Honey Nut Cheerios, Reese's Puffs and Rice Chex

• Cinnamon Toast Crunch, Cocoa Puffs, Frosted Flakes, Honey Nut Cheerios, Reese's Puffs and Rice Chex

Multiple Choice

Which shows the sample space for flipping two coins?

• H, T

• HH, HT, TH, TT

• HH, TT

• Dime, Nickel

Defining Sample Space

Sample spaces can also be represented with tree diagrams. Tree diagrams are
useful when determining the outcomes for compound probability events.

Compound probability events measure the likelihood of multiple events
occurring.

When using visual representations to determine sample spaces, it is best to
begin with a tree diagram and then record that information in table or list form.

Creating Tree Diagrams

Example 1:

When ordering a combo, you can choose between three sandwiches (chicken,
turkey, and grilled cheese) and two sides (chips and fruit cup). What is the
probability of ordering a combo that contains turkey? Create a list, table and tree diagram then find the outcomes)

Creating Tree Diagrams

Example 2:

What are the possible outcomes of flipping a coin and rolling a die? Create a
tree diagram and find the outcomes

Draw

Create a tree diagram and put the number of outcomes

Multiple Choice

The cafeteria is serving three kinds of sandwiches:  tuna (T), chicken, (C), and peanut butter (P).  They are also serving a choice of two drinks:  milk (M) or water (W).  Which shows the complete set of possible combinations?

• TW, CW, PW

• TW, TM, TC, CW, PW

• TW, TM, CW, CM, PW, PM

• TCP, MW

Finding the number of outcomes

Multiple Choice

Which tree diagram has the most possible outcomes?

Multiple Choice

The daily special at the House of Pies offers one of three featured pies and your choice of coffee, tea, milk or juice. How many ways can you order the special?

• 12

• 8

• 15

• 6

Multiple Choice

If you choose 1 scoop of ice cream from 12 flavors and any 1 topping from a choice of 8, how many different ice-cream sundaes can you make?

• 58

• 96

• 20

• 192

Multiple Choice

What is the probability of randomly picking a lunch with pizza, soda, and ice cream?

• 1/18

• 3/18 or 1/6

• 13/18

• 1/3