Unit #: 6
Subject(s): Math 2
Grade(s): 9-12
Designer(s): Kristen Fye, Ashley Pethel, Megan Bell, Christy Bentley, Karen Mullins,
Elizabeth Smith
PREAMBLE
This unit builds on knowledge of basic probability learned in middle school. No changes were made from the 2015-2016 Math 2 Unit 6.
STAGE 1 – DESIRED RESULTS
Unit Title: Applications of Probability
Transfer Goal(s): Students will be able to independently use their learning to apply properties of independent, dependent and conditional probability.
Enduring Understandings:
Students will understand that…
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A sample space is the set of all possible outcomes
An event can be the complement, union or intersection of other
events
A two-way frequency table defines a sample space, which can be
used to find conditional probabilities and determine dependence or
independence of events.
Probability helps make determinations by evaluating decisions and
strategies.
The probability of an event’s occurrence can be predicted with
varying degrees of confidence.
Experimental probability gets closer to theoretical probability the
more trials you run.
Students will know:
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Multiplication Rule
Addition Rule
Difference between dependent and independent events
Permutations and Combinations (Honors)
Definition of theoretical and experimental probability
Probability notation: P(A), P(B), P(A  B), P (A  B), P(B|A)
Essential Questions:
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What is the difference between independent and dependent events?
What is conditional probability?
When is an event mutually exclusive?
How is the probability of an event determined and described?
What is the best representation of sample space?
Is theoretical probability accurate?
Students will be able to:
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Determine if an event is fair
Evaluate results of an event
Construct and interpret data from frequency tables
Make decisions based on probability
Make predictions based on data
Describe a sample space
Describe similarities and differences of complements, unions, and
intersections
Calculate probability of an event
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)
Last revision 9/8/16
1
Unit #: 6
Subject(s): Math 2
Grade(s): 9-12
Designer(s): Kristen Fye, Ashley Pethel, Megan Bell, Christy Bentley, Karen Mullins,
Elizabeth Smith
STAGE 1– STANDARDS
Common Core State Standards(s)
NC.M2.S.CP.1 Understand independence and conditional probability and
use them to interpret data
ACT Standards
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Compute straightforward probabilities for common situations
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Exhibit knowledge of conditional and joint probability
NC.M2.S.CP.4 Understand independence and conditional probability and
use them to interpret data
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Represent data on two categorical variables by
constructing a two-way frequency table of data. Interpret
the two-way table as a sample space to calculate
conditional, joint and marginal probabilities. Use the
table to decide if events are independent.
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Translate from one representation of data to another (ex. bar graph to
a circle graph)
Exhibit knowledge of conditional and joint probability
Describe events as subsets of the outcomes in a sample
space using characteristics of the outcomes or as unions,
intersections and complements of other events.
NC.M2.S.CP.3 Understand independence and conditional probability and
use them to interpret data
Develop and understand independence and conditional
probability.
a. Use a 2-way table to develop understanding
of the conditional probability of A given B (written
P(A|B)) as the likelihood that A will occur given that B
has occurred. That is, P(A|B) is the fraction of event B’s
outcomes that also belong to event A.
b. Understand that event A is independent from event B
if the probability of event A does not change in response
to the occurrence of event B. That is P(A|B)=P(A).
NC.M2.S.CP.5 Understand independence and conditional probability and  Exhibit knowledge of conditional and joint probability
use them to interpret data
Recognize and explain the concepts of conditional probability
and independence in everyday language and everyday
situations.
NC.M2.S.CP.6 Use the rules of probability to compute probabilities of
 Exhibit knowledge of conditional and joint probability
compound events in a uniform probability model
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.
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)
Last revision 9/8/16
2
Unit #: 6
Subject(s): Math 2
Grade(s): 9-12
Designer(s): Kristen Fye, Ashley Pethel, Megan Bell, Christy Bentley, Karen Mullins,
Elizabeth Smith
NC.M2.S.CP.7 Use the rules of probability to compute probabilities of
compound events in a uniform probability model
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.
NC.M2.S.CP.8 Use the rules of probability to compute probabilities of
compound events in a uniform probability model
(+) 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.
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Compute straightforward probabilities for common situations
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Exhibit knowledge of conditional and joint probability
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)
Last revision 9/8/16
3