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 above two times. The sum of their spins
determines whether they win.
Work with your team to determine probabilities of different outcomes by answering
the questions below.
a.
b.
c.
d.
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.
Chunky mix-in
Fruit swirl
Hazelnuts
Sprinkles
Toffee bits
Apricot
Plum
Berry
Grape
Base flavor
Vanilla
Chocolate
a. 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?
b. 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 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.
a. How many different flavor combinations are possible? Where do you look on the
diagram to count the number of complete combinations?
b. Use your probability tree to help you find the probability that Scott’s final
combination will include plum swirl.
c. 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.
a. 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.
b. Two events are mutually exclusive if they have no outcomes in common. Do
Scott’s sister and little brother have mutually exclusive events?
c. 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.
a. Draw a probability tree to organize the different outfit combinations Rona might
choose.
b. What is the probability that she will wear both a polka dot shirt and plaid pants?
c. What is the probability that she will not wear the black pants?
d. If it is possible, make a probability table for Rona’s outfits. Which way of
representing the outcomes do you like better?
e. Are the events polka dot and plaid mutually exclusive? Explain. .
f. Are the events polka dot and white mutually exclusive? Explain.
5-69. Represent all of the possible outcomes using a list, probability table, or
probability tree. Then find the indicated probability in each situation below.
a. Represent all the possible combinations of flipping a coin three times in a row. How
many combinations are there? What is the probability of getting heads exactly twice?
b. Represent all the possible combinations of spinning the two spinner. (Just
combinations, not sums). How many combinations are there? What is the probability
that exactly one spinner lands on 4?
c. At the car rental agency, you will be given either a truck or a sedan. Each model
comes in four colors: green, black, white, or tan. Represent all the possible
combinations. If there is one vehicle of each color for each model available, what is
the probability you will get a green truck?
5-70. LEARNING LOG
Describe the methods for organizing outcomes in a probability situation that you have
learned in the past few lessons, such as systematic lists, probability tables and
probability trees. Describe situations for which each tool is appropriate and any
advantages and disadvantages with using it. You may want to include an example
from your recent work to help you explain.