Common Core High School Statistics & Probability Teaching and Learning Resources
Domain: CP: Conditional Probability and the Rules of Probability
Select the cluster for resources on this page:
CPA: Understand independence and conditional probability
and use them to interpret data
Standards:
 CPA.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”).
 CPA.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.
 CPA.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.
 CPA.4. Construct and interpret twoway
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 and to approximate
conditional probabilities. For example, collect data from a
random sample of students in your school on their favorite subject
among math, science, and English. Estimate the probability that a
randomly selected student from your school will favor science given
that the student is in tenth grade. Do the same for other subjects
and compare the results.
 CPA.5. Recognize and explain the concepts
of conditional probability and independence in everyday language and
everyday situations. For example, compare the chance of having
lung cancer if you are a smoker with the chance of being a smoker if
you have lung cancer.
Technologyenhanced investigations:
Stattrek.com Statistics Dictionary contains the following key vocabulary for this domain.
Select the term from the Stattrek pulldown menu. Use with CPA,
CPB:
addition rule 
complement 
independent 
sample space 
Bayes' theorem/rule 
conditional probablity 
intersection 
twoway table (frequency) 
combination; permutation 
event 
multiplication rule 
union 
Art of Problem Solving:
Counting and Probability Videos: These are the videos that go with
each of the sections within the 14chapter textbook,
Introduction to Counting & Probability.
Cut the Knot: Applet:
Conditional Probability and Independent Events: This applet is
an interactive tool that helps learners to grasp the definition and the
significance of conditional probabilities and independent events.
Use with CPA.3.
LearnZillion:
 Lesson set:
Describe events as subsets of a sample space: Five video
lessons: Organize sample space information, identify the
intersection and union of two events, identify the complement of
an event, determine quantities belonging to subsets of a sample
space. Aligns with CPA.1.
 Lesson set:
Describe events as subsets of a sample space, or as unions,
intersections, or complements of other events: Five video
lessons: Describe a sample space by organizing the set of all
possible outcomes, describe an event and its complement,
describe the intersection of two events, describe the union of
two or more events, describe the complement, union, and
intersection of events in a word problem. Aligns with
CPA.1.
 Lesson set:
Describe events as subsets of a sample space, or as unions,
intersections, or complements of other events: Five video
lessons: Describe events as subsets of a sample space, determine
the probability of an event and its complement; determine the
probability of union and intersection of several events, compare
the probability of union and intersection of events.
Aligns with CPA.1.
 Lesson set:
Understand independence and determine whether events are
independent: Three video lessons: Determine whether events
are independent, determine independence using a formula,
calculate the probability of independent events. Aligns
with CPA.2.
 Lesson set:
Understand and determine independence: Four video lessons:
Determine whether events are independent or associated,
determine whether events are independent within a twoway table,
determine independence using products of probabilities,
understand selecting without replacement. Aligns with
CPA.2.
 Lesson set:
Understand conditional probability and use it to determine
independence: Three video lessons: Understand conditional
probability, compute conditional probability using a formula,
determine independence using conditional probability.
Aligns with CPA.3.
 Lesson set:
Understand the conditional probability of A given B as P(A and
B)/P(B): Four video lessons: Interpret conditional
probabilities; identify conditional probability in a twoway
table and in a treediagram; interpret independent variables
using conditional probabilities. Aligns with CPA.3.
 Lesson set:
Recognize and explain the concepts of conditional probability
and independence: Four video
lessons: Understand conditional probability using scenarios,
calculate conditional probabilities, determine dependent or
independent by comparing scenarios, prove independence
numerically by using the independence formula. Aligns with CPA.5.
Purple Math: Venn Diagrams: Introduction, Logic and set notation, Set notation
exercises, Venn word problems. Use with CPA.1.
MIT BLOSSOMS: Video lessons with additional teacher and learner
resources. Descriptions are from the video summaries.
 Flu Math Games:
"This video lesson shows students that math can play a role in
understanding how an infectious disease spreads and how it can be
controlled." Additional simulations are included. Aligns
with Algebra standards SSEB.3.c and REIA.1; Function standards
IFC.8.b, BFB.4.a, and LEA1.(a, c); and Statistics and Probability
standards IDB.6.a, ICA.1, ICB.4, CPA.2, and MDA.1.

The Monty Hall Problem or How to Outsmart a Game Show and Win a
Car: "This lesson teaches students how to make decisions in
the face of uncertainty by using decision trees. It is aimed for
high school kids with a minimal background in probability; the
students only need to know how to calculate the probability of two
uncorrelated events both occurring (ie flipping 2 heads in a row).
Over the course of this lesson, students will learn about the role
of uncertainty in decision making, how to make and use a decision
tree, how to use limiting cases to develop an intuition, and how
this applies to everyday life." Aligns with CPA.2, CPB.8,
CPB.9, MDB.5.a, MDB.6, and MDB.7.
Stat Trek: Tutorials:
Wolfram Demonstrations Project:
Download the free Wolfram CDF player
to interact with the following manipulatives. Note: Within the
Wolfram Demonstration Project are
12 manipulatives addressing CPA.1,
7 manipulatives for CPA.2,
6 manipulatives for CPA.3,
1 manipulative for
CPA.4,
7 manipulatives for CPA.5. Among those:

Monty Hall Paradox: Aligns with CPA.1, CPA.2, CPA.3,
CPA.5, and MDB.6.

Multiplying Probabilities: Aligns with CPA.1, CPB.9.

Probabilities of Matching Colors: Involves multiplication of
probabilities. Aligns with CPA.1, CPB.9.

Conditional Probability: Aligns with CPA.1, CPA.2, CPA.3,
CPA.5, and CPB.6.

Venn Diagrams: This shows all 127 nonempty unions and intersections of three sets.
You can show or hide the corresponding set notation, given in
terms of union, intersection, and complement. Aligns with CPA.1, CPB.6, CPB.7.

Probability of Being Sick After Having Tested Positive for a
Disease (Bayes' Rule): Aligns with CPA.3, CPA.4, CPA.5,
MDB.7.
Wolfram MathWorld:
Zweigmedia.com: Tutorials and examples using fillin or
multiple choice to test understanding. Learners can also choose to
do game versions of some topics. Use with CPA:
Multiple Choice:
CK12:
Venn Diagrams: Use Venn diagrams to describe situations when problem
solving. Practice questions with review content and video. Aligns
with CPA.1.
Khan Academy:
Probability unit. Practice questions with videos.
MathsIsFun.com:

Probability: Complement Contains a concise explanation of
the complement, outcomes that are "not" the event, with worked
examples. Following the explanation are ten multiple choice
exercises. Use with CPA.1.

Probability: Independent Events Contains a concise
explanation of the independent events with worked examples.
Following the explanation are ten multiple choice exercises.
Use with CPA.2.

Dependent Events: Conditional Probability Contains a
concise explanation of the conditional probability and dependent
events with worked examples. Following the explanation are ten
multiple choice exercises. Use with CPA.3.
Constructedresponse:
Khan Academy:
Probability unit. Practice questions with videos.
Performance tasks:
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CPB: Use the rules of probability to compute
probabilities of compound events.
Standards:
 CPB.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.
 CPB.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.
 CPB.8. (+) Apply the general
Multiplication Rule in a uniform probability model, P(A and B) =
P(A)P(BA) = P(B)P(AB), and interpret the answer in terms of the model.
 CPB.9. (+) Use permutations and
combinations to compute probabilities of compound events and solve problems.
Technologyenhanced investigations:
Art of Problem Solving:
Counting and Probability Videos: These are the videos that go with
each of the sections within the 14chapter textbook,
Introduction to Counting & Probability.
Cut the Knot:
Bayes' Theorem: Bayes' Theorem is used as a direct application of
conditional probability of A given B: P(AB) = P(A∩B)
/ P(B). Three practical examples are provided with solutions. Use with CPB.6.
Omnicalculator.com: Statistics calculators include a Probability
Calculator and Bayes' Theorem Calculator. Explanation of theory is
included for each.
Study.com: College Math: Probability
and Statistics: 11 video lessons. Each includes sample problems and a quiz. View
the probability lessons to "learn about types of events that express
probability, including simple, compound, complementary, independent and
dependent. You'll learn what the outcomes of these events are and how
you can calculate said probability. Other topics covered include the 'at
least one' rule of independent events, permutations, math combinations
and more." Use with CPB.
LearnZillion:
 Lesson set:
Find the conditional probability of A given B as the fraction of
B's outcomes that also belong to A: Two video lessons:
Understand conditional probability, calculate conditional
probabilities using a twoway table. Aligns with CPB.6.
 Lesson set:
Apply the addition rule: Two video lessons: Use addition
rule to calculate the probability of disjoint event A or B,
nondisjoint events and the addition rule, solve word problems
using the addition rule, calculate probabilities by using the
complement and addition rule, use conditional probability,
calculate different probabilities by working backward using the
addition rule. Aligns with CPB.7.
MIT BLOSSOMS: Video lesson with additional teacher and learner
resources. Description is from the video summary.
The Monty Hall Problem or How to Outsmart a Game Show and Win a
Car: "This lesson teaches students how to make decisions in
the face of uncertainty by using decision trees. It is aimed for
high school kids with a minimal background in probability; the
students only need to know how to calculate the probability of two
uncorrelated events both occurring (ie flipping 2 heads in a row).
Over the course of this lesson, students will learn about the role
of uncertainty in decision making, how to make and use a decision
tree, how to use limiting cases to develop an intuition, and how
this applies to everyday life." Aligns with CPA.2, CPB.8,
CPB.9, MDB.5.a, MDB.6, and MDB.7.
Webmath.com: Permutations. Verify
your list of permutations for up to 8 entries.
Wolfram Demonstrations Project:
Download the free Wolfram CDF player
to interact with the following manipulatives. Note: Within the
Wolfram Demonstration Project are
6 manipulatives addressing CPB.6,
5 manipulatives for CPB.7,
6 manipulatives for CPB.8,
23 manipulatives for CPB.9. Among those:

Conditional Probability: Aligns with CPA.1, CPA.2, CPA.3,
CPA.5, and CPB.6.

Venn Diagrams: This shows all 127 nonempty unions and intersections of three sets.
You can show or hide the corresponding set notation, given in
terms of union, intersection, and complement. Aligns with CPA.1, CPB.6, CPB.7.

Venn Diagrams for two sets: Aligns with CPB.6, CPB.7.

The perfect Venn Diagram: Aligns with CPB.6, CPB.7.

Urn sampling with or without replacement: Aligns with
CPB.7, CPB.8.

Probabilities of permutations: To calculate the probability of a selected sequence of results
from a series of independent events, multiply the probabilities
of each selected result occurring together. Aligns with
CPB.8, CPB.9.

Probabilities of combinations:
Order does not matter. Aligns with CPB.8, CPB.9.

Permutations: There are n! ways to arrange n
elements. Aligns with CPB.9.

Number of handshakes: Aligns with CPB.9.

Binomial probability distribution: Aligns with CPB.9.

Clinking wineglasses: Aligns with CPB.9.

Expanding a set of possibilities: Uses combinations of
different choices to make ice cream desserts. Aligns with
CPB.9.

Pascal's triangle: Aligns with CPB.9, APRC.5.
YouTube videos:
GCSE Probability
Part 1: This video is from a professor in Great Britain who nicely
explains probability and shows examples: expected frequency, the typical
problems involving picking balls from a bag, mutually exclusive events,
independent events, and drawing diagrams to help identify possibilities.
Probability
Part 2: tree diagrams. The same professor in Great Britain
discusses the balls in a bag problems when making two picks, which
leads to tree diagrams to help determine probability involving
replacing after each pick, and then not replacing after a pick.
Zweigmedia.com: Tutorials and examples using fillin or
multiple choice to test understanding. Learners can also choose to
do game versions of some topics. Use with CPB:
Multiple Choice:
MathsIsFun.com:
 Mutually Exclusive Events: Contains a concise explanation of
the Addition Rule with examples for events that are mutually
exclusive and not mutually exclusive. Following the
explanation are ten multiple choice exercises. Use with
CPB.7.
 Probability Tree Diagrams: Contains explanation of the use
of tree diagrams and the multiplication principle to calculate
probabilities of independent and dependent events.
Following the explanation are ten multiple choice exercises.
Use with CPB.8.
 Permutations and Combinations: Contains a concise
explanation of the concepts and formulas used to calculate
permutations and combinations. Following the explanation
are ten multiple choice exercises. There is a
Permutations and Combinations Calculator. Use with CPB.9.
Constructedresponse:
Khan Academy: Practice questions with videos.
L. Spector: The Math Page: Topics in Precalculus: Use with CPB.9:

Factorials: The concept of factorials and working with those is
needed for calculating permutations and combinations.
 Permutations and Combinations: These lessons help learners to
understand the concepts of permutations and combinations and include
practice problems with answers provided.
Performance tasks:
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Common Core Math:
Intro  HS Statistics & Probability Domain:
ID  IC  CP  MD 