AP STATISTICS Unit 5: Probability
Enduring understanding (Big Idea): Students will understand randomness; the concepts and rules of probabilities; how to use simulation to estimate
probabilities, probability models and their use to describe chance behavior; and conditional probabilities and independence.
Essential Questions:
1.
What is a random phenomenon, when do we need to consider it and
6. For continuous variables, what is the probability of a precise value occurring?
how can we investigate it using probability and simulation?
7. How do we determine if a given probability distribution is valid?
2. How is the likelihood of a random event occurring related to the long8. How can we perform a simulation by use of a random number table, a
term frequency of occurrence of the event?
calculator or software to investigate the likelihood of an outcome occurring?
3. What is the sample space of a random phenomenon?
9. What is a joint probability? How do we use its properties to solve problems?
4. For a finite number of outcomes, how do we use the multiplication
10. What are the probability rules and how do we use them to determine if two
principle to determine the number of outcomes?
events are disjoint and/or complementary, find the probabilities of unions and
5. How do we construct Tree diagrams, Venn diagrams and Two-way
intersections, and find the joint probability of two events??
tables to organize visually the use of the multiplication and addition
11. What is a conditional probability, how do we find it, and how do we use it to
rules to determine the probabilities of events?
determine potential causes of events?
6. For continuous variables, how do we use geometric areas to find
12. What is the property of Independence, and how is it related to Conditional
probabilities (areas under density curves) of events (intervals on the
Probabilities?
horizontal axis) and for determine the likelihood of an event?
13. Are mutually exclusive events independent? Why or why not?
BY THE END OF THIS UNIT:
Students will know: (See the AP Statistics Course Description page 7 for details)
Students will be able to
AP Stats IE Exploring categorical data
1. Interpret probability as a long-run relative frequency
AP Stats IIIA Exploring random phenomena using probability and simulation (20%–30%)
2. Describe probability models for chance behaviors
Vocabulary: Complement, Conditional probability, Conditional probability formula,
Disjoint, Event, General addition rule for two events General multiplication rule,
Independent events (independence), Intersection, Mutually exclusive, Outcome,
Probability, Probability model, Sample space, Simulation, Tree diagram, Union, Venn
diagram
Unit Resources: (see Fathom, Applets and Glossary in Unit #3)
Learning Tasks: homework - see page 5-5 of the Teacher's Edition
Performance Task: "FRAPPY" (see Formative Assessments below)
Project: "Casino Labs” by Daren Starnes at
http://apstatsmonkey.com/StatsMonkey/Probability_files/Casino%20Lab%2008.pdf
With solutions at
http://apstatsmonkey.com/StatsMonkey/Probability_files/Casino%20Lab%2008%20Solutions.pdf
Or if Casino games are not desired , use just the last activity in the above files & use the applet at
www.stat.sc.edu/~west/javahtml/LetsMakeaDeal.html
Unit Review Game: Jeopardy and Millionaire (PowerPoints)
http://www.apstatsmonkey.com/StatsMonkey/TPS3e.html
3. Use Venn or tree diagrams, Two Way Tables, or simulation to
model chance behaviors
4. Use probability rules; including the complement rule, and the
addition rule for mutually exclusive events
5. Determine if events are independent
6. Use the general addition and general multiplication rules for
chance behaviors, for either independent or not events
Mathematical Practices in Focus:
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of
others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
AP STATISTICS Unit 5: Probability
CORE CONTENT
Cluster Title: B. Summarize, represent, and interpret data on two categorical and quantitative variables (S-ID)
Standards:
S.ID.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data
(including joint, marginal, and conditional relative frequencies)…
Cluster Title: D. Understand and evaluate random processes underlying statistical experiments (S-IC)
S.IC.2 Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation
Cluster Title: F. Understand independence and conditional probability and use them to interpret data (S-CP)
S.CP.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.4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the twoway table as a sample space to decide if events are independent …
Cluster Title: G. Use the rules of probability to compute probabilities of compound events in a uniform probability model (S-CP)
S.CP.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
Cluster Title: I. Use probability to evaluate outcomes of decisions (S-MD)
S.MD.6 (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator)
S.MD.7 (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a
game)
For Sections 5.1 & 5.2
NCSCOC 3.05 Apply concepts of probability to solve problems
NCSCOC 3.07 http://www.dpi.state.nc.us/curriculum/mathematics/scos/2003/9-12/72apstatistics
AP Stats IE2 Exploring categorical data … joint frequencies for two-way tables
AP Stats IIIA1-3, 5 1 Interpreting probability, including long-run relative frequency interpretation; 2 “Law of Large Numbers” concept, 3 Addition
rule…; 5 Simulation of random behavior and probability distributions
Concepts and Skills to Master (on paper and with technology)
Section 5.1
[Randomness, Probability and Simulation]
 The Idea of Probability
 Myths about randomness
 Simulations
Section 5.2
[Probability Rules]
 Probability Models
 Basic rules of probability
 Two-way tables and probability
 Venn Diagrams and probability
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
AP STATISTICS Unit 5: Probability
SUPPORTS FOR TEACHERS
Critical Background Knowledge
Prior material in this course contained in Units 1 – 4 (i.e. Chapters 1-4)
Academic Vocabulary
Complement, Disjoint, Event, General addition rule for two events, Intersection, Mutually exclusive, Outcome, Probability, Probability model, Sample space,
Simulation, Union, Venn diagram
Suggested Instructional Strategies









Rely on the Teachers' Edition and the Platinum Resource Binder
The text is excellent and students should have their book (and their calculator) at each
class. The challenge is how to inspire kids to read and study it. There should be class
discussions during each class using material from the book and using the calculator.
Consider assigning the next class' material as a prereading. Especially focus on the boxes
labeled "AP Exam Common Error" in the margins (and also in Appendix A)
Begin with a discussion of the Case Study on page 281 and lay a foundation for power
Do Activities on pages 284, 287
Do Activities on pages 215 and 220, followed by a technology simulation of the activity.
Have a Class Discussion of the Rules for Simulation on page 289 and add rules to deal
with repeats, out-of-range outcomes and stopping. Discuss the table on page 290 as
examples of these rules (Very Important)
Have a Class Discussion of Section 5.1's "Summary" on page 292 and Section 5.2's
"Summary” on page 308
The College Board has posted tremendously helpful material
http://apcentral.collegeboard.com/apc/public/courses/teachers_corner/2151.html
in particular use:
http://apcentral.collegeboard.com/apc/members/exam/exam_information/8357.html
Useful directories for the released questions are at
http://www.apstatsmonkey.com/StatsMonkey/AP_Review.html
for FR look for AP Index 11_12.xls
for MC look for MC_Index.xls - Daren Starnes
Resources
 Textbook Correlation:
Chapter 5 , Introduction and Section 1 (pages
280 - 298)
Chapter 5, Section 2 (pages 299 - 311)
 Most of the PowerPoint slides on the Instructor's
CD are very helpful.
 Use resources at
http://apstatsmonkey.com/StatsMonkey/Statsmo
nkey.html
 Monitor the AP Statistics List Serve [see Electronic
Discussion Groups on
http://apcentral.collegeboard.com/apc/public/co
urses/teachers_corner/2151.html ] soon to be an
AP community see
https://epl.collegeboard.org/epl/login.do
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
AP STATISTICS Unit 5: Probability
Sample Formative Assessment Tasks
Skill-based tasks



CHECK YOUR UNDERSTANDING (textbook pages 286, 292,
303, and 305)
Use assessments at http://www.stats4stem.org/
Use Released Multiple Choice questions (see the last Suggested
Instructional Strategy above for a link to the list of MC questions).
The column "% correct” shows the global performance on the AP
Exam for that question. Add a column to the spreadsheet to keep a
record of the questions you used and when used.
Problem Tasks


At the End of Sections 5.1 and/or 5.2 students in collaborative student
groups could determine solutions to relevant AP released Free response
questions. Then provide each group with the model solution and have
them update their solution if needed. Selected group should present their
problem and updated solution to the class describing what they learned
from their discussions
For a list of free response questions that you could use. Go to
http://www.apstatsmonkey.com/StatsMonkey/AP_Review.html
Look for the link AP Index 11_12.xls. (Do not use 2003B #2 until the
end of Chapter 5.) Add a column to the spreadsheet and keep a record
of the questions you used and when used.
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
AP STATISTICS Unit 5: Probability
CORE CONTENT
Cluster Title: B. Summarize, represent, and interpret data on two categorical and quantitative variables (S-ID)
Standards:
S.ID.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data
(including … conditional relative frequencies)…
Cluster Title: F. Understand independence and conditional probability and use them to interpret data (S-CP)
S.CP.2 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.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.4 … Use the two-way table as a sample space to approximate conditional probabilities …
S.CP.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations
Cluster Title: G. Use the rules of probability to compute probabilities of compound events in a uniform probability model (S-CP)
S.CP.6 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.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.
Cluster Title: I. Use probability to evaluate outcomes of decisions (S-MD)
S.MD.7 (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a
game)
For Sections 5.3
NCSCOC 3.05 Apply concepts of probability to solve problems
NCSCOC 3.07 Simulate sampling distributions http://www.dpi.state.nc.us/curriculum/mathematics/scos/2003/9-12/72apstatistics
AP Stats IE Exploring categorical data 3. Conditional relative frequencies and association
AP Stats IIIA 3 … multiplication rule, conditional probability and independence
Concepts and Skills to Master (on paper and with technology)
Section 5.3
[Conditional Probability ]
 Conditional Probability and Independence
 Independence: A special multiplication rule
 Tree diagrams and the general multiplication rule
 Calculating Conditional Probabilities
SUPPORTS FOR TEACHERS
Critical Background Knowledge
Previous Skills and concepts in this course from Chapter 1 through Section 5.3
Academic Vocabulary
Conditional probability, Conditional probability formula, General multiplication rule, Independent events (Independence), Tree diagram
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
AP STATISTICS Unit 5: Probability
Suggested Instructional Strategies








Sample Formative Assessment Tasks
Skill-based tasks



CHECK YOUR UNDERSTANDING (pages 314, 317, 321,
and 323)
Use assessments at http://www.stats4stem.org/

Use Released Multiple Choice questions (see the last Suggested
Instructional Strategy above for a link to the list of MC questions)
See suggestion for usage in Unit # 3
Use Quizzes at
http://bcs.whfreeman.com/tps4e/#628644__630756__
Do the Chapter 5 AP Statistics Practice Test on page 336

Use ARTIST SCALE - Probability

Resources
Rely on the Teachers' Edition and the Platinum Resource Binder
 Textbook Correlation:
The text is excellent and students should have their book (and their calculator) at each 
Chapter 5, Section 3 (pages 312- 337)
class. The challenge is how to inspire kids to read and study it. There should be class
 Most of the PowerPoint slides on the Instructor's
discussions during each class using material from the book and using the calculator.
CD are very helpful.
Consider assigning the next class' material as a prereading. Especially focus on the boxes
 Use resources at
labeled "AP Exam Common Error" in the margins (and also in Appendix A)
http://apstatsmonkey.com/StatsMonkey/Statsmonkey.
Do Activity on page 206 (except just have cards with questions about basic statistics and
html
do an Observational Study of the # the student got correct, i.e. an Observational Study"

Monitor the AP Statistics List Serve [see Electronic
Do Activities on pages 215 and 220, followed by a technology simulation of the activity.
Discussion Groups on
Have a Class Discussion of the General Multiplication rule on page 319 and of the
http://apcentral.collegeboard.com/apc/public/course
Conditional Probability Formula on page 324. Have the class determine what the rules
would be if the prior events were event B
s/teachers_corner/2151.html ] soon to be an AP
Have Class Discussions of Section 5.3's "Summary" on page 328
community see
The College Board has posted tremendously helpful material (continued)
https://epl.collegeboard.org/epl/login.do
http://apcentral.collegeboard.com/apc/public/courses/teachers_corner/2151.html
in particular use:
http://apcentral.collegeboard.com/apc/members/exam/exam_information/8357.html
Useful directories for the released questions are at
http://www.apstatsmonkey.com/StatsMonkey/AP_Review.html
for FR look for AP Index 11_12.xls
for MC look for MC_Index.xls - Daren Starnes
Problem Tasks

At the End of Unit 5 do FRAPPY #6a [which uses 2003B #2]:
http://apstatsmonkey.com/StatsMonkey/TPS3e_files/Frappy6a.pdf
(Or as an alternate, see the last Suggested Instructional Strategy above
for a list of free response questions that you could alternately use as
your FRAPPY. Go to
http://www.apstatsmonkey.com/StatsMonkey/AP_Review.html
for the FR questions. Look for the link AP Index 11_12.xls.
Add a column to the spreadsheet and keep a record of the questions you
used and when used.)

To Use Frappies: On the first page at
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.
AP STATISTICS Unit 5: Probability
http://ore.gen.umn.edu/artist/tests/index.html

Use Released Multiple Choice questions (see the last Suggested
Instructional Strategy above for a link to the list of MC questions).
The column "% correct " shows the global performance on the
AP Exam for that question. Add a column to the spreadsheet to
keep a record of the questions you used and when used.
http://apstatsmonkey.com/StatsMonkey/FRAPPYs.html click on the
FRAPPY Presentation to learn about them and how to use them as
Formative Assessments. (Click on the Frappy Presentation to Advance
to a new slide. You may also download handout notes using the link to
the right)
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.