**Unit 6: Applications of Probability**
*Ever played darts? Geometric probability helps us understand the
likelihood of hitting the bull’s-eye. Ever taken a train or a bus to
meet a friend? Geometric probability helps us understand your likelihood
of arriving on time. This course ends by revisiting probability,
building on concepts learned in previous grades but now using geometric
probability models where possible. You will use set theory to compute
and interpret theoretical and experimental probabilities of compound
events, examining mutually exclusive events, independent events, and
conditional probability. You will then apply this knowledge to make
informed decisions and evaluation decisions made using
probability.[**[6]**](#_ftn1)*

[6]Ibid

**Unit 6 Time Advisory**

Completing this unit should take you approximately 12 hours, 30
minutes.

☐ Subunit 6.1: 4 hours, 30 minutes

☐ Subunit 6.2: 8 hours

**Unit6 Learning Outcomes**

Upon successful completion of this unit, you will be able to:

- Identify and explain independence and conditional probability.
- Use independence and conditional probability to interpret data using
two-way tables.
- Apply the rules of probability to compute the probabilities of
compound events.
- Evaluate the outcomes of decisions using probability.

Standards Addressed (*Common Core*):

- CCSS.Math.Content.HSS-CP.A.1
- CCSS.Math.Content.HSS-CP.A.2
- CCSS.Math.Content.HSS-CP.A.3
- CCSS.Math.Content.HSS-CP.A.4
- CCSS.Math.Content.HSS-CP.A.5
- CCSS.Math.Content.HSS-CP.B.6
- CCSS.Math.Content.HSS-CP.B.7
- CCSS.Math.Content.HSS-CP.B.8
- CCSS.Math.Content.HSS-CP.B.9
- CCSS.Math.Content.HSS-MD.B.6
- CCSS.Math.Content.HSS-MD.B.7
- CCSS.ELA-Literacy.RST.9-10.3
- CCSS.ELA-Literacy.RST.9-10.4
- CCSS.ELA-Literacy.RST.9-10.5
- CCSS.ELA-Literacy.WHST.9-10.1d
- CCSS.ELA-Literacy.WHST.9-10.1e

**6.1 Independent and Dependent Events**
In this subunit, you will review the basic concepts of probability and
how they relate to your everyday life. You will examine the probability
of independent events taking place—earning an A in Spanish class and
earning a B in Biology, for example. You will also examine the
probability of dependent events—having a day off and going to an art
museum, for example. The concepts of mutually exclusive and mutually
inclusive events are related to this. When determining the probability
of several events, these terms are important to understand in order to
avoid double counting. The resources in this subunit provide explanatory
content as well as practice problems that allow you to receive immediate
feedback on your progress and understanding.

**6.1.1 Venn Diagrams**
- **Explanation: CK-12: Basic Probability and Statistics Concepts—A
Full Course: “Venn Diagrams”**
Link: CK-12: *Basic Probability and Statistics Concepts—A Full
Course*: “Venn
Diagrams” (HTML)

Instructions: Please click on the link above, and watch the three
videos provided. Next read the information that follows the videos,
take notes, and complete the examples as you go. Answers follow each
example. The guided practice and practice problems are optional, as
this course provides you with practice from other sources. Upon
reviewing this section, you should be able to read Venn diagrams and
use them to demonstrate the various possible outcomes of an
experiment.

Completing this activity should take approximately 30 minutes.

Standards Addressed (*Common Core*):

```
●
[CCSS.Math.Content.HSS-CP.A.1](http://www.corestandards.org/Math/Content/HSS/CP/A/1)
●
[CCSS.Math.Content.HSS-CP.A.5](http://www.corestandards.org/Math/Content/HSS/CP/A/5)
●
[CCSS.ELA-Literacy.RST.9-10.3](http://www.corestandards.org/ELA-Literacy/RST/9-10/3)
●
[CCSS.ELA-Literacy.WHST.9-10.1e](http://www.corestandards.org/ELA-Literacy/WHST/9-10/1/e)
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
```

**Web Media: YouTube: Khan Academy’s “Probability with Playing Cards and Venn Diagrams”**Link: YouTube: Khan Academy’s “Probability with Playing Cards and Venn Diagrams” (YouTube)

Instructions: Please click on the link above, watch the video, and take notes, following along with the examples the presenter provides. This video examines the use of Venn diagrams with playing cards.

Completing this activity should take approximately 15 minutes.

Standards Addressed (*Common Core*):● CCSS.Math.Content.HSS-CP.A.1

● CCSS.Math.Content.HSS-CP.A.5

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.**Did I Get This? Activity: Khan Academy’s “Probability 1”**Link: Khan Academy’s “Probability 1” (HTML)

Instructions: Please click on the link above. This page provides a series of practice problems that allow you to calculate basic probability in a variety of situations. Each question has explanations worked out step-by-step if you need hints along the way. The program monitors your success, and when you have correctly completed about six questions consecutively, it will tell you that you are ready to move on to a new skill.

Completing this activity should take approximately 15 minutes.

Standards Addressed (*Common Core*):● CCSS.Math.Content.HSS-CP.A.1

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

**6.1.2 Independent Events and Sample Spaces**
- **Explanation: CK-12: Basic Probability and Statistics Concepts—A
Full Course: “Independent Events and Sample Spaces”**
Link: CK-12: *Basic Probability and Statistics Concepts—A Full
Course*: “Independent Events and Sample
Spaces” (HTML)

Instructions: Please click on the link above, and watch the three
videos provided. Next read the information that follows the videos,
take notes, and complete the examples as you go. Answers follow each
example. The guided practice and practice problems are optional, as
this course provides you with practice from other sources. Upon
reading this section, you should be able to identify independent
events and calculate the probability of an outcome of independent
events taking place.

Completing this activity should take approximately 30 minutes.

```
Standards Addressed (*Common Core*):
●
[CCSS.Math.Content.HSS-CP.A.1](http://www.corestandards.org/Math/Content/HSS/CP/A/1)
●
[CCSS.Math.Content.HSS-CP.A.2](http://www.corestandards.org/Math/Content/HSS/CP/A/2)
●
[CCSS.ELA-Literacy.RST.9-10.3](http://www.corestandards.org/ELA-Literacy/RST/9-10/3)
●
[CCSS.ELA-Literacy.WHST.9-10.1e](http://www.corestandards.org/ELA-Literacy/WHST/9-10/1/e)
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
```

**Did I Get This? Activity: Khan Academy’s “Independent Probability”**Link: Khan Academy’s “Independent Probability” (HTML)

Instructions: Please click on the link above. This page provides a series of practice problems that allow you to calculate the probability independent events. Each question has explanations worked out step-by-step if you need hints along the way. The program monitors your success, and when you have correctly completed about six questions consecutively, it will tell you that you are ready to move on to a new skill.

Completing this activity should take approximately 15 minutes.

Standards Addressed (*Common Core*):● CCSS.Math.Content.HSS-CP.A.1

● CCSS.Math.Content.HSS-CP.A.2

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

**6.1.3 Dependent Events and Sample Spaces**
- **Explanation: CK-12: Basic Probability and Statistics Concepts—A
Full Course: “Dependent Events and Sample Spaces”**
Link: CK-12: *Basic Probability and Statistics Concepts—A Full
Course*: “Dependent Events and Sample
Spaces” (HTML)

Instructions: Please click on the link above, and watch the three
videos provided. Next read the information that follows the videos,
take notes, and complete the examples as you go. Answers follow each
example. The guided practice and practice problems are optional, as
this course provides you with practice from other sources. Upon
reading this section, you should be able to identify dependent
events and calculate the probability of an outcome involving such
events.

Completing this activity should take approximately 30 minutes.

Standards Addressed (*Common Core*):

```
●
[CCSS.Math.Content.HSS-CP.A.1](http://www.corestandards.org/Math/Content/HSS/CP/A/1)
●
[CCSS.Math.Content.HSS-CP.A.2](http://www.corestandards.org/Math/Content/HSS/CP/A/2)
●
[CCSS.ELA-Literacy.RST.9-10.3](http://www.corestandards.org/ELA-Literacy/RST/9-10/3)
●
[CCSS.ELA-Literacy.WHST.9-10.1e](http://www.corestandards.org/ELA-Literacy/WHST/9-10/1/e)
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
```

**Did I Get This? Activity: Khan Academy’s “Dependent Probability”**Link: Khan Academy’s “Dependent Probability” (HTML)

Instructions: Please click on the link above. This page provides a series of practice problems that allow you to calculate the probability of dependent events. Each question has explanations worked out step-by-step if you need hints along the way. The program monitors your success, and when you have correctly completed about six questions consecutively, it will tell you that you are ready to move on to a new skill.

Completing this activity should take approximately 15 minutes.

Standards Addressed (*Common Core*):● CCSS.Math.Content.HSS-CP.A.1

● CCSS.Math.Content.HSS-CP.A.2

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

**6.1.4 Mutually Exclusive Events**
- **Explanation: CK-12: Basic Probability and Statistics Concepts—A
Full Course: “Mutually Exclusive Events”**
Link: CK-12: *Basic Probability and Statistics Concepts—A Full
Course*: “Mutually Exclusive
Events” (HTML)

Instructions: Please click on the link above, and watch the two
videos provided. Next read the information that follows the videos,
take notes, and complete the examples as you go. Answers follow each
example. The guided practice and practice problems are optional, as
this course provides you with practice from other sources. Upon
reading this section, you should be able to identify mutually
exclusive events and calculate the probability of outcomes in such
events.

Completing this activity should take approximately 30 minutes.

Standards Addressed (*Common Core*):

```
●
[CCSS.Math.Content.HSS-CP.A.1](http://www.corestandards.org/Math/Content/HSS/CP/A/1)
●
[CCSS.Math.Content.HSS-CP.A.2](http://www.corestandards.org/Math/Content/HSS/CP/A/2)
●
[CCSS.Math.Content.HSS-CP.A.4](http://www.corestandards.org/Math/Content/HSS/CP/A/4)
●
[CCSS.ELA-Literacy.RST.9-10.3](http://www.corestandards.org/ELA-Literacy/RST/9-10/3)
●
[CCSS.ELA-Literacy.WHST.9-10.1e](http://www.corestandards.org/ELA-Literacy/WHST/9-10/1/e)
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
```

**6.1.5 Mutually Inclusive Events**
- **Explanation: CK-12: Basic Probability and Statistics Concepts—A
Full Course: “Mutually Inclusive Events”**
Link: CK-12: *Basic Probability and Statistics Concepts—A Full
Course*: “Mutually Inclusive
Events” (HTML)

Instructions: Please click on the link above, and watch the three
videos provided. Next read the information that follows the videos,
take notes, and complete the examples as you go. Answers follow each
example. The guided practice and practice problems are optional, as
this course provides you with practice from other sources. Upon
reading this section, you should be able to identify mutually
inclusive events and calculate the probability of outcomes in such
events.

Completing this activity should take approximately 30 minutes.

Standards Addressed (*Common Core*):

```
●
[CCSS.Math.Content.HSS-CP.A.1](http://www.corestandards.org/Math/Content/HSS/CP/A/1)
●
[CCSS.Math.Content.HSS-CP.A.2](http://www.corestandards.org/Math/Content/HSS/CP/A/2)
●
[CCSS.Math.Content.HSS-CP.B.7](http://www.corestandards.org/Math/Content/HSS/CP/B/7)
●
[CCSS.ELA-Literacy.RST.9-10.3](http://www.corestandards.org/ELA-Literacy/RST/9-10/3)
●
[CCSS.ELA-Literacy.WHST.9-10.1e](http://www.corestandards.org/ELA-Literacy/WHST/9-10/1/e)
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
```

**Web Media: YouTube: Khan Academy’s “Addition Rule for Probability”**Link: YouTube: Khan Academy’s “Addition Rule for Probability” (YouTube)

Instructions: Please click on the link above, watch the video, and take notes, following along with the examples the presenter provides. This video examines the addition rule for probability and how it works for mutually inclusive and mutually exclusive events.

Completing this activity should take approximately 15 minutes.

Standards Addressed (*Common Core*):● CCSS.Math.Content.HSS-CP.A.1

● CCSS.Math.Content.HSS-CP.A.2

● CCSS.Math.Content.HSS-CP.A.5

● CCSS.Math.Content.HSS-CP.B.7

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.**Checkpoint: Mathematics Assessment Project: “Medical Testing”**Link: Mathematics Assessment Project: “Medical Testing” (HTML)

Instructions: Please click on the link above, and scroll down to the section of the lesson entitled “Resources.” Download the PDF file underneath “Lesson (complete).” The assessment is on pages S-1 and S-2 and is titled “Medical Testing.” Complete the questions to the best of your ability. The chart and questions on page S-2 are hints to help you answer the questions. When you are finished, use the solutions on pages T-12 through T-14 to check your understanding. For an additional challenge, scroll down to the sample responses. Questions are provided to guide you in the analysis of the work and in making improvements to each sample.

Completing this activity should take approximately 45 minutes. The extension will add another 30 minutes.

Standards Addressed (*Common Core*):

● CCSS.Math.Content.HSS-CP.A.1

● CCSS.Math.Content.HSS-CP.A.2

● CCSS.Math.Content.HSS-CP.A.3

● CCSS.Math.Content.HSS-CP.A.4

● CCSS.Math.Content.HSS-CP.A.5

● CCSS.Math.Content.HSS-CP.B.6

● CCSS.Math.Content.HSS-MD.B.6

● CCSS.Math.Content.HSS-MD.B.7

● CCSS.ELA-Literacy.RST.9-10.3

● CCSS.ELA-Literacy.RST.9-10.4

● CCSS.ELA-Literacy.RST.9-10.5

● CCSS.ELA-Literacy.WHST.9-10.1d

● CCSS.ELA-Literacy.WHST.9-10.1e

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

**6.2 Conditional Probability**
This subunit builds on the previous section. You will examine
permutations and combinations, looking at how order may affect the
probability (as with permutations) or may not affect the probability (as
with combinations). You can use permutations to examine the probability
of correctly guessing your locker combination or to decide how many
different groups of 4 your teacher can arrange from your class of 24
students. Additionally, you will examine conditional probability, which
exists when the probability of the second event depends on the outcome
of the first event. The resources in this subunit provide explanatory
content as well as practice problems that allow you to receive immediate
feedback on your progress and understanding.

**6.2.1 Tree Diagrams**
- **Explanation: CK-12: Basic Probability and Statistics Concepts—A
Full Course: “Tree Diagrams”**
Link: CK-12: *Basic Probability and Statistics Concepts—A Full
Course*: “Tree
Diagrams” (HTML)

Instructions: Please click on the link above, and watch the three
videos provided. Next read the information that follows the videos,
take notes, and complete the examples as you go. Answers follow each
example. The guided practice and practice problems are optional, as
this course provides you with practice from other sources. Upon
completing this section, you should be able to read and create tree
diagrams to illustrate the possible outcomes of an event.

Completing this activity should take approximately 30 minutes.

Standards Addressed (*Common Core*):

```
●
[CCSS.Math.Content.HSS-CP.A.5](http://www.corestandards.org/Math/Content/HSS/CP/A/5)
●
[CCSS.Math.Content.HSS-CP.B.7](http://www.corestandards.org/Math/Content/HSS/CP/B/7)
●
[CCSS.Math.Content.HSS-CP.B.8](http://www.corestandards.org/Math/Content/HSS/CP/B/8)
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
```

**Activity: Connexions: Kenny M. Felder’s “Probability Homework—Homework: Tree Diagrams”**Link: Connexions: Kenny M. Felder’s “Probability Homework—Homework: Tree Diagrams” (HTML)

Instructions: Please click on the link above, and complete the practice problems. This activity will provide you with the opportunity to create tree diagrams that represent the possible outcomes of a variety of events.

Completing this activity should take approximately 30 minutes.

Standards Addressed (*Common Core*):● CCSS.Math.Content.HSS-CP.A.5

● CCSS.Math.Content.HSS-CP.B.6

● CCSS.Math.Content.HSS-CP.B.7

● CCSS.Math.Content.HSS-CP.B.8

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

**6.2.2 Permutations and Combinations Compared**
- **Explanation: CK-12: Basic Probability and Statistics Concepts—A
Full Course: “Permutations and Combinations Compared”**
Link: CK-12: *Basic Probability and Statistics Concepts—A Full
Course*: “Permutations and Combinations
Compared” (HTML)

Instructions: Please click on the link above, and watch the three
videos provided. Next read the information that follows the videos,
take notes, and complete the examples as you go. Answers follow each
example. The guided practice and practice problems are optional, as
this course provides you with practice from other sources. Upon
reading this section, you should be able to identify permutations
and use them to determine the total number of arrangements possible
in an ordered set of objects.

Completing this activity should take approximately 30 minutes.

Standards Addressed (*Common Core*):

```
●
[CCSS.Math.Content.HSS-CP.B.6](http://www.corestandards.org/Math/Content/HSS/CP/B/6)
●
[CCSS.Math.Content.HSS-CP.B.9](http://www.corestandards.org/Math/Content/HSS/CP/B/9)
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
```

**Did I Get This? Activity: Khan Academy’s “Permutations and Combinations”**Link: Khan Academy’s “Permutations and Combinations” (HTML)

Instructions: Please click on the link above. This page provides a series of practice problems that allow you to calculate the probability of events involving permutations and combinations. Each question has explanations worked out step-by-step if you need hints along the way. The program monitors your success, and when you have correctly completed about six questions consecutively, it will tell you that you are ready to move on to a new skill.

Completing this activity should take approximately 30 minutes.

Standards Addressed (*Common Core*):● CCSS.Math.Content.HSS-CP.B.6

● CCSS.Math.Content.HSS-CP.B.9

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

**6.2.3 Permutation Problems**
- **Explanation: CK-12: Basic Probability and Statistics Concepts—A
Full Course: “Permutation Problems”**
Link: CK-12: *Basic Probability and Statistics Concepts—A Full
Course*: “Permutation
Problems” (HTML)

Instructions: Please click on the link above, and watch the two
videos provided. Next read the information that follows the videos,
take notes, and complete the examples as you go. Answers follow each
example. The guided practice and practice are optional, as this
course provides you with practice from other sources. Upon reading
this section, you should be able to solve problems requiring the use
of permutations.

Completing this activity should take approximately 30 minutes.

Standards Addressed (*Common Core*):

```
●
[CCSS.Math.Content.HSS-CP.B.6](http://www.corestandards.org/Math/Content/HSS/CP/B/6)
●
[CCSS.Math.Content.HSS-CP.B.9](http://www.corestandards.org/Math/Content/HSS/CP/B/9)
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
```

**Did I Get This? Activity: Khan Academy’s “Permutations”**Link: Khan Academy’s “Permutations” (HTML)

Instructions: Please click on the link above. This page provides a series of practice problems that allow you to calculate the probability of events involving permutations. Each question has explanations worked out step-by-step if you need hints along the way. The program monitors your success, and when you have correctly completed about six questions consecutively, it will tell you that you are ready to move on to a new skill.

Completing this activity should take approximately 30 minutes.

Standards Addressed (*Common Core*):● CCSS.Math.Content.HSS-CP.B.6

● CCSS.Math.Content.HSS-CP.B.9

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

**6.2.4 Permutations with Repetition**
- **Explanation: CK-12: Basic Probability and Statistics Concepts—A
Full Course: “Permutations with Repetition”**
Link: CK-12: *Basic Probability and Statistics Concepts—A Full
Course*: “Permutations with
Repetition” (HTML)

Instructions: Please click on the link above, and watch the two
videos provided. Next read the information that follows the videos,
take notes, and complete the examples as you go. Answers follow each
example. The guided practice and practice problems are optional, as
this course provides you with practice from other sources. Upon
reading this section, you should be able to identify permutations
with repetition and calculate the probability of outcomes in such
events.

Completing this activity should take approximately 30 minutes.

Standards Addressed (*Common Core*):

```
●
[CCSS.Math.Content.HSS-CP.B.6](http://www.corestandards.org/Math/Content/HSS/CP/B/6)
●
[CCSS.Math.Content.HSS-CP.B.9](http://www.corestandards.org/Math/Content/HSS/CP/B/9)
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
```

**Checkpoint: CK-12: Basic Probability and Statistics Concepts—A Full Course: “Permutation Problems Exercises”**Link: CK-12:*Basic Probability and Statistics Concepts—A Full Course*: “Permutation Problems Exercises” (HTML)Instructions: Please click on the link above, and then click on the tab labeled “Exercises.” This page will test your knowledge of permutations by providing you with a series of multiple-choice questions on the topic. Take your time and be sure you have scratch paper available to complete the calculations. Upon submitting each answer, the program will provide you with immediate feedback. For questions that you answer incorrectly, take a few minutes to understand your error and the correct answer.

Completing this activity should take approximately 30 minutes.

Standards Addressed (*Common Core*):

● CCSS.Math.Content.HSS-CP.B.6

● CCSS.Math.Content.HSS-CP.B.9

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

**6.2.5 Combinations**
- **Explanation: CK-12: Basic Probability and Statistics Concepts—A
Full Course: “Combinations”**
Link: CK-12: *Basic Probability and Statistics Concepts—A Full
Course*:
“Combinations” (HTML)

Instructions: Please click on the link above, and watch the three
videos provided. Next read the information that follows the videos,
take notes, and complete the examples as you go. Answers follow each
example. The guided practice and practice problems are optional, as
this course provides you with practice from other sources. Upon
reading this section, you should be able to identify combinations
and calculate the probability of outcomes in such events.

Completing this activity should take approximately 30 minutes.

Standards Addressed (*Common Core*):

```
●
[CCSS.Math.Content.HSS-CP.B.6](http://www.corestandards.org/Math/Content/HSS/CP/B/6)
●
[CCSS.Math.Content.HSS-CP.B.9](http://www.corestandards.org/Math/Content/HSS/CP/B/9)
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
```

**6.2.6 Combination Problems**
- **Explanation: CK-12: Basic Probability and Statistics Concepts—A
Full Course: “Combination Problems”**
Link: CK-12: *Basic Probability and Statistics Concepts—A Full
Course*: “Combination
Problems” (HTML)

Instructions: Please click on the link above, and watch the two
videos provided. Next read the information that follows the videos,
take notes, and complete the examples as you go. Answers follow each
example. The guided practice and practice problems are optional, as
this course provides you with practice from other sources. Upon
reading this section, you should be able to solve problems involving
combinations.

Completing this activity should take approximately 30 minutes.

Standards Addressed (*Common Core*):

```
●
[CCSS.Math.Content.HSS-CP.B.6](http://www.corestandards.org/Math/Content/HSS/CP/B/6)
●
[CCSS.Math.Content.HSS-CP.B.9](http://www.corestandards.org/Math/Content/HSS/CP/B/9)
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
```

**Did I Get This? Activity: Khan Academy’s “Combinations”**Link: Khan Academy’s “Combinations” (HTML)

Instructions: Please click on the link above. This page provides a series of practice problems that allow you to calculate the probability of outcomes in events involving combinations. Each question has explanations worked out step-by-step if you need hints along the way. The program monitors your success, and when you have correctly completed about six questions consecutively, it will tell you that you are ready to move on to a new skill.

Completing this activity should take approximately 30 minutes.

Standards Addressed (*Common Core*):● CCSS.Math.Content.HSS-CP.B.6

● CCSS.Math.Content.HSS-CP.B.9

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.**Checkpoint: CK-12: Basic Probability and Statistics Concepts—A Full Course: “Combination Problems Exercises”**Link: CK-12:*Basic Probability and Statistics Concepts—A Full Course*: “Combination Problems Exercises” (HTML)

Instructions: Please click on the link above, and then click on the tab labeled “Exercises.” This page will test your knowledge of combinations by providing you with a series of multiple-choice questions on the topic. Take your time and be sure you have scratch paper available to complete the calculations. Upon submitting each answer, the program will provide you with immediate feedback. For questions that you answer incorrectly, take a few minutes to understand your error and the correct answer.

Completing this activity should take approximately 30 minutes.

Standards Addressed (*Common Core*):

● CCSS.Math.Content.HSS-CP.B.9

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

**6.2.7 Conditional Probability**
- **Explanation: CK-12: Basic Probability and Statistics Concepts—A
Full Course: “Conditional Probability”**
Link: CK-12: *Basic Probability and Statistics Concepts—A Full
Course*: “Conditional
Probability” (HTML)

Instructions: Please click on the link above, and watch the three
videos provided. Next read the information that follows the videos,
take notes, and complete the examples as you go. Answers follow each
example. The guided practice and practice problems are optional, as
this course provides you with practice from other sources. Upon
reading this section, you should be able to identify conditional
probability and calculate the probability of outcomes in such
events.

Completing this activity should take approximately 30 minutes.

Standards Addressed (*Common Core*):

```
●
[CCSS.Math.Content.HSS-CP.B.6](http://www.corestandards.org/Math/Content/HSS/CP/B/6)
●
[CCSS.Math.Content.HSS-CP.B.9](http://www.corestandards.org/Math/Content/HSS/CP/B/9)
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
```

**Interactive Lab: Shodor: “Advanced Monty Hall”**Link: Shodor: “Advanced Monty Hall” (Java)

Instructions: Please click on the link above, where you will see a page with four tabs. Click on the tab labeled “Learner,” and then download the worksheets titled “Advanced Monty Hall Exploration Questions” and “Monty Hall Tally Table.” Next, click on the tab labeled “Activity” to complete the activity. The “Help” tab provides further instructions on how the activity works if you have difficulties.

Completing this activity should take approximately 45 minutes.

Standards Addressed (*Common Core*):● CCSS.Math.Content.HSS-CP.A.5

● CCSS.Math.Content.HSS-CP.B.6

● CCSS.Math.Content.HSS-CP.B.9

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.**Checkpoint: CK-12: Basic Probability and Statistics Concepts—A Full Course: “Conditional Probability Exercises”**Link: CK-12:*Basic Probability and Statistics Concepts—A Full Course*: “Conditional Probability Exercises” (HTML)

Instructions: Please click on the link above, and then click on the tab labeled “Exercises.” This page will test your knowledge of conditional probability by providing you with a series of multiple-choice questions on the topic. Take your time and be sure you have scratch paper available to complete the calculations. Upon submitting each answer, the program will provide you with immediate feedback. For questions that you answer incorrectly, take a few minutes to understand your error and the correct answer.

Completing this activity should take approximately 30 minutes.

Standards Addressed (*Common Core*):

● CCSS.Math.Content.HSS-CP.B.6

● CCSS.Math.Content.HSS-CP.B.9

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

**Final Exam**
- **Final Exam: The Saylor Foundation's “K12MATH010 Final Exam”**
Link: The Saylor Foundation's “K12MATH010 Final
Exam” (HTML)

Instructions: You must be logged into your Saylor Foundation School
account in order to access this exam. If you do not yet have an
account, you will be able to create one, free of charge, after
clicking the link. A number of the questions in this exam are
accompanied by geometrical figures. Please note that these figures
are not drawn to scale. Be assured, however, that the labels and
values provided alongside these figures will be sufficient to help
you answer these questions. Additionally, several of the questions
in this exam are derived from the Real World
Math Area of Study
on Saylor.org. If you need additional help studying for this exam,
you may find additional content on the topics presented in this
course in RWM103: Geometry.