Simple and Compound Probability Tree Diagrams

Unit 4: Probabilistic Reasoning
Lesson 4: Using Expressions to Calculate
Compound Probability (Part 1)

Learning Standards

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

a. Understand that, just as with simple events, the probability of a
compound event is the fraction of outcomes in the sample space
for which the compound event occurs.

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 use a visual aid to determine probabilities of compound
events.

●

I can understand the concept that the probability of a compound
event is a fraction of the possible outcomes.

●

I can analyze a situation to determine if compound events are
occurring.

Multiple Choice

Theoretical Probability is?

• What should happen

• What does happen

• What actually happens

• What I want to Happen

Multiple Choice

Experimental Probability is:

• What will happen 

• What actually happens

• What should happen

• What I think happens

Multiple Choice

If this 8-section spinner is spun 120 times, how many times would one expect to land on an even number?

• 75

• 45

• 15

• 40

Multiple Choice

An event that consists of two or more events

•  event

• dependent events

• experiment

• compound event

Finding Sample Space

Consider the experiment: Flip a coin, and then roll a number cube.

Elena, Kiran, and Priya each use a different method for finding the sample space of this
experiment

Elena carefully writes
a list of all the options:

Heads 1, Heads 2, Heads
3, Heads 4, Heads 5,
Heads 6, Tails 1, Tails 2,
Tails 3, Tails 4, Tails 5,
Tails 6.

Kiran makes a table:

Priya draws a tree with branches in
which each pathway represents a
different outcome:

Determining the number of outcomes

Multiple Choice

Which tree diagram has the most possible outcomes?

Multiple Choice

Which of the following situations is represented by this tree diagram?

• 3 shirt options, 6 pants options, and 12 shoe options

• 3 shirt options, 2 pants options, and 2 shoe options

• 2 shirt options, 3 pants options, and 1 shoe option

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

The Standard Automotive car company offers its midsize car with 2 doors, 4 doors, or as a convertible. The car is available in 3 exterior colors and 2 interior colors. Find the number of different midsize cars the company can produce.

• 12

• 18

• 36

• 24

Using visual representations for compound

probability

What is the probability of landing heads on a fair coin and rolling a 2 on a
fair, standard number cube?

Elena

Heads 1, Heads 2, Heads

3, Heads 4, Heads 5,

Heads 6, Tails 1, Tails 2,
Tails 3, Tails 4, Tails 5,

Tails 6.

Kiran

Priya

Multiple Choice

The tree diagram shows the outcomes of rolling a die and flipping a coin.  
What is the probability of rolling an even number and flipping a head?

• ³/₁₂

• ¹/₂

• ⁴/₁₂

• ⁰/₁₂

Represent Tree Diagram With Visuals

What is the probability of selecting an outfit that has a top with short sleeves and bottoms
that are shorts from the options pictured?

Represent Tree Diagram With Expressions, Ex. 1

What is the probability of spinning blue and then picking a green marble?

Three fair coins are tossed simultaneously.

a)write the sample space as ordered triples

b)Find P(all tails)

c)Find P(exactly 2 tails)

d)Find P(at least one head)

Represent Tree Diagram With Expressions, Ex. 2

Multiple Choice

What is the probability of the spinning both and getting A and 1?

• $$\frac{1}{3}$$

• $$\frac{1}{5}$$

• $$\frac{2}{7}$$

• $$\frac{1}{12}$$

Multiple Choice

What is the probability of rolling a 3 and spinning a red?

• 1/6

• 1/4

• 1/10

• 1/24