Common Core Geometry Unit 5 Starting Points
Unit 5: Applications of Probability
Essential Questions:
● How can a sample space be designed to represent possible outcomes?
● How can Venn diagrams and two-way tables be used to determine probabilities of
compound events? How can these tools be used to determine if events are
independent?
● What strategies might be used to find the probability of mutually exclusive
(disjoint) events? Mutually inclusive (overlapping) events?
● How can you find the probabilities of complements, unions, and intersections?
● What is conditional probability? How can you find the conditional probabilities?
● What does it mean for two events to be independent in the context of the
problem?
● When should the addition rule be used? What do the results mean in the context
of the problem?
● What is the multiplication rule and how should it be used? (GT only)
● How can you determine if a situation is best modeled using permutations or
combinations? How can permutations and combinations be used to calculate
probabilities? (GT only)
● How can probabilities be used to analyze and make fair decisions? (GT only)
Curriculum Standards:
Understand independence and conditional probability and use them to interpret
data.
S.CP.A.1 Describe events as subsets of a sample space (the set of outcomes) using
characteristics (or categories) of the outcomes, or as unions, intersections, or
complements of other events (“or”, “and”, “not”).
S.CP.A.2 Understand that two events A and B are independent if the probability of A and
B occurring together is the product of their probabilities, and use this characterization to
determine if they are independent.
S.CP.A.3 Understand the conditional probability of A given B as P(A and B)/P(B), and
interpret independence of A and B as saying that the conditional probability of A given B
is the same as the probability of A, and the conditional probability of B given A is the
same as the probability of B.
S.CP.A.4 Construct and interpret two-way frequency tables of data when two categories
are associated with each object being classified. Use the two-way table as a sample space
to decide if events are independent and to approximate conditional probabilities.
S.CP.A.5 Recognize and explain the concepts of conditional probability and
independence in everyday language and everyday situations.
This document represents one sample starting points for the unit. It is not all-inclusive and is only
one planning tool. Please refer to the wiki for more information and resources.
Use the rules of probability to compute probabilities of compound events in a
uniform probability model.
S.CP.B.6 Find the conditional probability of A given B as the fraction of B’s outcomes
that also belong to A, and interpret the answer in terms of the model.
S.CP.B.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret
the answer in terms of the model.
S.CP.B.8 (+) Apply the general Multiplication Rule in a uniform probability model, P(A
and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.
S.CP.B.9 (+) Use permutations and combinations to compute probabilities of compound
events and solve problems.
Use probability to evaluate outcomes of decisions.
S.MD.B.6 (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a
random number generator).
S.MD.B.7 (+) Analyze decisions and strategies using probability concepts (e.g., product
testing, medical testing, pulled a hockey goalie at the end of a game).
Part I: Probability of Compound Events
Approximate Length: 7-10 days (6-8 G/T)
Standard(s)
Days
Notes
S.CP.A.1
Big Ideas:
3-4
S.CP.B.7
Generate a sample space for a given compound
event (using lists, tree diagrams, etc.).
Use Venn diagrams and two-way tables to
examine probabilities of compound events.
Review notation for probabilities, unions,
intersections and complements.
Introduce concepts of mutually exclusive
(disjoint) and mutually inclusive (overlapping)
events. Represent examples with Venn
diagrams.
Use Venn diagrams to derive the addition rule
for compound events.
Find probabilities of intersections, unions, and
complements.
This document represents one sample starting points for the unit. It is not all-inclusive and is only
one planning tool. Please refer to the wiki for more information and resources.
Resources:
 Lesson: Unions, Intersections and
Complements
 Lesson: Addition Rule of Probability
Assessment Items:
 Illustrative Mathematics: But Mango is
My Favorite
S.CP.A.2
S.CP.A.4
4-6
Big Ideas:
Define independence of compound events.
Examine examples to determine if the events are
independent.
Construct and use two-way tables to find
probabilities of compound events (probabilities
out of the total number of outcomes.)
Resources:
 Task: Sample Space
 Lesson Seed: Independent and
Dependent Events
 Task: All the Pets
Assessment Items:
 Illustrative Mathematics: Cards and
Independence
 Illustrative Mathematics: Rain and
Lightning
Part II: Conditional Probability
Approximate Length: 15-18 days (27-29 G/T)
Standard(s)
Days
Notes
S.CP.A.3
Big Ideas:
6-8
S.CP.A.5
Introduce conditional probability.
Use two-way tables to find conditional
probabilities.
Use conditional probability to determine if two
events are independent.
This document represents one sample starting points for the unit. It is not all-inclusive and is only
one planning tool. Please refer to the wiki for more information and resources.
Explain what conditional probability and
independence means in the context of the
problem.
Resources:
 Lesson: Conditional Probability
 Lesson Seed: Conditional Probability
and Independence
Assessment Items:
 Illustrative Mathematics: The Titanic 2
 Illustrative Mathematics: Lucky
Envelopes
 Illustrative Mathematics: Breakfast
Before School
S.CP.B.6
S.CP.A.4
6-8
Big Ideas:
Calculate conditional probabilities.
Examine examples to determine if the events are
independent.
Construct and use two-way tables to find
conditional probabilities.
Resources:
 Task: Common Characteristics
 Task: Favorite Baseball Teams
Assessment Items:
 Illustrative Mathematics: The Titanic 1
 Illustrative Mathematics: The Titanic 3
 Illustrative Mathematics: How Do You
Get to School
S.CP.B.8 (+) (GT only)
2-3
Big Ideas:
Derive and use the multiplication rule.
Interpret probabilities in terms of the situation.
Resources:
 Task: Fun Spinner
This document represents one sample starting points for the unit. It is not all-inclusive and is only
one planning tool. Please refer to the wiki for more information and resources.
S.CP.B.9 (+) (GT only)
3-5
Big Ideas:
Introduce scenarios to emphasize the difference
in sample space for permutations and
combinations.
Derive formulas for permutations and
combinations.
Use permutations and combinations to calculate
probabilities.
Resources:
 Lesson: Permutations and Combinations
Assessment Items:
 Illustrative Mathematics: Return to
Fred’s Fun Factory
 Illustrative Mathematics: Random
Walk III
 Illustrative Mathematics: Random
Walk IV
 Illustrative Mathematics: Alex, Mel,
and Chelsea Play a Game
S.MD.B.6 (+) (GT only)
S.MD.B.7 (+) (GT only)
3-5
Big Ideas:
Describe how to design for a simulation to
produce fair results.
Calculate probabilities to determine if the
scenario is fair.
Evaluate probability results to make decisions.
Resources:
 Task: Seating Chart
 Task: Baseball Outfielders
 Task: Golden Ticket
Assessment Items:
 Illustrative Mathematics: Fred’s Fun
Factory
This document represents one sample starting points for the unit. It is not all-inclusive and is only
one planning tool. Please refer to the wiki for more information and resources.
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs
3.0 Unported License.
This document represents one sample starting points for the unit. It is not all-inclusive and is only
one planning tool. Please refer to the wiki for more information and resources.