Lesson 5.2.5
HW: 5-71 to 5-75
Learning Target: Scholars will continue creating systematic lists and probability tables and will learn to
use probability trees to model outcomes for compound events. They will calculate probabilities for
multiple independent events where both outcomes are desired. Scholars will be introduced to the term
“mutually exclusive.”
In this
lesson you will work with different models for organizing outcomes of multiple events when both one
event and another event occur. Throughout this lesson, use these questions to help focus your team’s
discussion.
 Is there more than one event?
 Do both one event and other events occur?
 Are the events independent?
5-65. THE DOUBLE SPIN
A giant wheel is divided into 5 equal sections labeled –2, –1, 0, 1, and 3. At the Double Spin, players
spin the wheel shown at right two times. The sum of their spins determines whether they win. Explore
using 5-65 Spinner eTool (CPM).
Work with your team to determine probabilities of different outcomes by answering the questions below.
1.
2.
3.
4.
 Make a list of the possible sums you could get.
Which sum do you think will be the most probable?
Create a probability table that shows all possible outcomes for the two spins.
If Tabitha could choose the winning sum for the Double Spin game, what sum would you advise
her to choose? What is the probability of her getting that sum with two spins?
5-66. Scott’s job at Crazy Creations Ice Cream Shop is to design new ice cream flavors. The company
has just received some new ingredients and Scott wants to be sure to try all of the possible
combinations. He needs to choose one item from each category to create the new flavor.
1. Without talking with your teammates, list three different combinations Scott could try. Make
sure you use the word “and.” Then share your combinations with your study team. How many
different combinations did you find? Do you think you found all of the possibilities?
2.
Creating a list of all of the possibilities would take time and require a lot
of writing the same words over and over. Because there are more than two options, a probability
table is also challenging. An alternative is creating a probability tree to show the different
combinations. A probability tree, like the one started at right and on the Lesson 5.2.5 Resource
Page, shows the different possibilities branching off each other. In this case, the two segments on
the left show the base flavors. Each different mix-in choice branches off of the base flavor, and
each fruit swirl branches off each mix-in choice. The first letter of each choice is used to label
this diagram.
The bold line in the diagram shows the combination vanilla, toffee bits and plum swirl. Complete
the probability tree to show all of the possible combinations.
3. How many different flavor combinations are possible? Where do you look on the diagram to
count the number of complete combinations?
4. Use your probability tree to help you find the probability that Scott’s final combination will
include plum swirl.
5. What is the probability that his final combination will include hazelnuts?
5-67. Scott’s sister loves hazelnuts and Scott’s little brother loves grape.
1. Recall that events are favorable outcomes. List all of the outcomes in Scott’s sister’s event. List
all the outcomes in Scott’s little brother’s event.
2. Two events are mutually exclusive if they have no outcomes in common. Do Scott’s sister and
little brother have mutually exclusive events?
3. What would two mutually exclusive events in the Crazy Creations Ice-Cream Shop be?
5-68. In a power outage, Rona has to reach into her closet in the dark to get dressed. She is going to find
one shirt and one pair of pants. She has three different pairs of pants hanging there: one black, one
brown, and one plaid. She also has two different shirts: one white and one polka dot.
1.
2.
3.
4.
Draw a probability tree to organize the different outfit combinations Rona might choose.
What is the probability that she will wear both a polka dot shirt and plaid pants?
What is the probability that she will not wear the black pants?
For what kinds of problems can you also make a probability table? If it is possible, make a
probability table for Rona’s outfits. Which way of representing the outcomes do you like better?
5. Are the events polka dot and plaid mutually exclusive? Explain. .
6. Are the events polka dot and white mutually exclusive? Explain.
5-71. WALKING THE DOG. Marcus and his brother always argue about who will walk the
dog. Their father wants to find a random way of deciding who will do the job. He invented a
game to help them decide. Each boy will have a bag with three colored blocks in it: one yellow,
one green, and one white. Each night before dinner, each boy draws a block out of his bag. If
the colors match, Marcus walks the dog. If the two colors do not match, his brother walks the
dog. Marcus’s father wants to be sure that the game is fair. Help him decide. 5-71 bag 1 HW
eTool (CPM) and 5-71 bag 2 HW eTool (CPM).
1. Make a probability tree of all of the possible combinations of draws that Marcus
and his brother could make. How many possibilities are there?
2. What is the probability that the boys will draw matching blocks? Is the game
fair? Justify your answer.
5-72. For Shelley’s birthday on Saturday, she received:
o
o
o
Two new shirts (one plaid and one striped);
Three pairs of shorts (tan, yellow, and green); and,
Two pairs of shoes (sandals and tennis shoes).
On Monday she wants to wear a completely new outfit. How many possible outfit choices does
she have from these new clothes? Draw a diagram to explain your reasoning.
5-73. In 2009, the federal government budget was $3.1 trillion ($3,100,000,000,000). The
government was looking to cut costs.
6. If it decided to cut 1%, how much money did it cut?
7. If the government reduced the budget by 7%, how much money did it cut?
8. If the government eliminated $93 billion ($93,000,000,000) from the budget, what
percentage did it cut?
5-74. Evaluate each expression.
9. 7 + (–3)
10. (10)(–5)
11. –5 + 6
12. (–2) ÷ (–2)
5-75. Write expressions for the perimeter and the area of this algebra tile shape. Then simplify
each expression by combining like terms.
Lesson 5.2.5

5-65. See below:
1. −4, −3, −2, −1, 0, 1, 2, 3, 4, 6
2. Answers vary.
3. See table below.
4. She should choose either −1 or 1. Each has a probability of

5-66. See below:
1. Answers vary. Probably not all possibilities will be found.
or 16%.
2. See answer diagram below.
3. 24 combinations. Count the number of branch ends at the right of the diagram.
4.
=
= 0.25 = 25%
5.
=
= 0.3 = 33
%

5-67. See below:
1. Sister: VHA, VHP, VHB, VHG, CHA, CHP, CHB, CHG. Brother: VHG, VSG,
VTG, CHG, CSG, CTG
2. No, they have VHG and CHG in common.
3. Answers vary, some possibilities are vanilla and chocolate, or berry and grape.

5-68. See below:
1. See possible diagram below.
2.
3.
4. See table below. When there are exactly two events that occur at the same time.
5. No. You could wear plaid pants and a polka dot shirt.
6. Yes, because you could not wear a polka dot shirt and a white shirt at the same
time.