**Unit 5: Probability and Statistics**
*Imagine that you would like to open a new business, but you need data
on what the local people would think and whether the business would be
successful. Your work on probability and statistics will help you build
an appropriate sample for surveying and show you how to use your data to
analyze the results and make predictions.*

*In this unit, you will begin by finding the probability of single
events. This will lead to the probability of compound events. You will
draw inferences based on random sampling, compare multiple samples, and
build representations of events using tables and tree diagrams. From the
models, you will make predictions and calculate the measure of center
and variability.*

**Unit 5 Time Advisory**

Completing this unit should take approximately 11 hours and 30
minutes.

☐ Subunit 5.1: 5 hours and 30 minutes

☐ Subunit 5.2: 2 hours and 15 minutes

☐ Subunit 5.3: 3 hours and 45 minutes

**Unit5 Learning Outcomes**

Upon successful completion of this course, you will be able to:
- Solve problems involving basic and compound probabilities.

- Make predictions about an event based on theoretical and
experimental probabilities.

- Use data from random samples to make inferences about a
population.

- Calculate the measures of center and variability.

- Create tree diagrams and organized lists to represent sample
spaces.

- Develop models to represent the probability of different events
occurring.

Standards Addressed (*Common Core*):
- CCSS.Math.Content.7.SP.A.1
- CCSS.Math.Content.7.SP.A.2
- CCSS.Math.Content.7.SP.B.3
- CCSS.Math.Content.7.SP.B.4
- CCSS.Math.Content.7.SP.C.5
- CCSS.Math.Content.7.SP.C.6
- CCSS.Math.Content.7.SP.C.7
- CCSS.Math.Content.7.SP.C.8
- CCSS.ELA-Literacy.RST.6-8.2
- CCSS.ELA-Literacy.RST.6-8.3
- CCSS.ELA-Literacy.RST.6-8.4
- CCSS.ELA-Literacy.RST.6-8.7
- CCSS.ELA-Literacy.WHST.6-8.1b
- CCSS.ELA-Literacy.WHST.6-8.4

**5.1 Probability**
*“There is a 30% chance of rain for Friday.” The chance of something
happening is the probability of an event occurring. Probabilities are
used to help make decisions. A 30% chance of rain is a fairly low
probability of occurring. A 90% chance of rain tells us that it is most
likely going to rain. We may need to cancel plans or at least remember
to bring an umbrella. In this subunit, you will take a look at how to
compute probabilities and how some events can affect the probability of
other events.*

**5.1.1 Basic Probability**
- **Explanation: Khan Academy’s “Basic Probability”**
Link: Khan Academy’s “Basic
Probability”
(YouTube)

Instructions: Watch the video to see the notation that is used when
writing probabilities and the three different forms that can be used
to write the probabilities.

Viewing this video should take approximately 15 minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.7.SP.C.5](http://www.corestandards.org/Math/Content/7/SP/C/5)
Terms of Use:This resource is licensed under a [Creative Commons
Attribution-NonCommercial-ShareAlike 3.0 Unported
License](http://creativecommons.org/licenses/by-nc-sa/3.0/). It is
attributed to Khan Academy.
```

**Activity: XP Math: “Plinko Probability - The Probability is Right”**Link: XP Math: “Plinko Probability - The Probability is Right” (Flash)

Instructions: In this game, you will answer probability questions about the amounts you are able to win. You will place your answer in the maroon box at the bottom right. The game will tell you whether your answer is correct. If the sound is on when you play the game, you will hear a noise for a wrong answer and you will not be given a chip. If you are correct, you will be given a chip to drop down the plinko board. The hint button places a triangle under each of the given values you need to answer the question. This way, you can count up the total to get the probability.

Playing this game should take approximately 15 minutes.

Standards Addressed (*Common Core*):Terms of Use:This resource is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

**Did I Get This? Activity: orgLib: “Preview Questions for Test: 7.SP.5 - Worksheet”**Link: orgLib: “Preview Questions for Test: 7.SP.5 - Worksheet” (HTML)

Instructions: Scroll down to the five questions and click on “Consume” beneath them. You will be brought to a new screen where you can type in your answers. After each question you will need to click on “Submit Answer.” When you have all five questions done, you will click on “Submit Test.” At this point, you will be brought to a screen that will show whether your answers are correct.

Completing this activity should take approximately 15 minutes.

Standards Addressed (*Common Core*):Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

**5.1.2 Compound Events**
- **Explanation: CK-12: “Probability of Compound Events”**
Link: CK-12: “Probability of Compound
Events”
(PDF)

Instructions: Read the section entitled “Guidance” to find the
difference between independent and dependent events. Be sure to take
note of how calculating the probability for a dependent event is
different from calculating the probability of an independent event.
Then solve the 17 practice questions at the bottom of the page.

Completing this activity should take approximately 45 minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.7.SP.C.8](http://www.corestandards.org/Math/Content/7/SP/C/8)
Terms of Use: This resource is licensed under a [Creative Commons
Attribution-NonCommercial-ShareAlike 3.0 Unported
License](http://creativecommons.org/licenses/by-nc-sa/3.0/). It is
attributed to CK-12 Foundation. The original version can be found
[here](http://www.ck12.org/probability/Probability-of-Compound-Events/lesson/Probability-of-Compound-Events/).
```

**5.1.2.1 Tree Diagrams, Organized Lists and Tables**
- **Explanation: Dr. Carol Fisher Burns’s “Probability Tree
Diagrams”**
Link: Dr. Carol Fisher Burns’s “Probability Tree
Diagrams”
(HTML)

Explanation: Read through the examples of probability questions and
take a look at the tree diagrams formed to answer the questions.
Then go back up to the top of the page and click on “Jump right to
the exercises!” This will bring you to a new screen where you can
practice making your own tree diagrams.

Making tree diagrams should take approximately 15 minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.7.SP.C.8](http://www.corestandards.org/Math/Content/7/SP/C/8)
Terms of Use: This resource is licensed under a [Creative Commons
Attribution-NonCommercial 2.5 Generic
License](http://creativecommons.org/licenses/by-nc/2.5/).
```

**Did I Get This? Activity: orgLib: “Preview Questions for Test: 7.SP.8 - Worksheet”**Link: orgLib: “Preview Questions for Test: 7.SP.8 - Worksheet” (HTML)

Instructions: Scroll down to the four questions and click on “Consume” beneath them. You will be brought to a new screen where you can type in your answers. After each question you will need to click on “Submit Answer.” When you have all four questions done, you will click on “Submit Test.” At this point, you will be brought to a screen that will show whether your answers are correct.

Completing this activity should take approximately 15 minutes.

Standards Addressed (*Common Core*):Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

**5.1.3 Experimental Probability**
- **Explanation: CK-12: “Experimental Probability”**
Link: CK-12: “Experimental
Probability”
(HTML)

Instructions: Read through the entire lesson on experimental
probability. Focus on the differences and similarities between your
hypothesis (theoretical probability) and the actual results
(experimental probability). You do not need to watch the video clip
after the reading. Instead, work through the questions in the “Time
to Practice” section.

Completing this activity should take approximately 1 hour and 15
minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.7.SP.C.6](http://www.corestandards.org/Math/Content/7/SP/C/6)
Terms of Use: This resource is licensed under a [Creative Commons
Attribution-NonCommercial-ShareAlike 3.0 Unported
License](http://creativecommons.org/licenses/by-nc-sa/3.0/).
```

**Activity: Shodor: “Experimental Probability”**Link: Shodor: “Experimental Probability” (HTML)

Instructions: Now is your chance to try out your own experiments. On this site there are several different interactive spinners. For three of the spinners, do the following:- 1. Calculate the theoretical probability of the spinner landing on red.
- 2. Complete 20 spins and keep track of the results.
- 3. Use the results to calculate the experimental probability of landing on red.
- 4. Compare the theoretical to the experimental probability.
- 5. Make a prediction: If you were to continue spinning the spinner 1,000 times, how many times would you expect the spinner to land on red?

Completing this activity should take approximately 45 minutes.

Standards Addressed (*Common Core*): - CCSS.Math.Content.7.SP.C.6Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

**Activity: Dan Meyer’s Three-Act Math Tasks: “Yellow Starbursts”**Link: Dan Meyer’s Three-Act Math Tasks: “Yellow Starbursts” (HTML)

Instructions: Follow the directions for the activity. There are videos and images to help you answer the questions. In Act 3, the answer will be provided and you will be given a chance to reflect on your work.

Completing this activity should take approximately 30 minutes.

Standards Addressed (*Common Core*):Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial 3.0 United States License. It is attributed to Day Meyer.

**Did I Get This? Activity: orgLib: “Preview Questions for Test: 7.SP.6 - Worksheet”**Link: orgLib: “Preview Questions for Test: 7.SP.6 - Worksheet” (HTML)

Instructions: Scroll down to the five questions and click on “Consume” beneath them. You will be brought to a new screen where you can type in your answers. After each question you will need to click on “Submit Answer.” When you have all five questions done, you will click on “Submit Test.” At this point, you will be brought to a screen that will show whether your answers are correct.

Completing this activity should take approximately 15 minutes.

Standards Addressed (*Common Core*):Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

**5.1.4 Geometric Probability**
- **Activity: GeoGebra: “A Look at Geometric Probability”**
Link: GeoGebra: “A Look at Geometric
Probability” (HTML)

Instructions: The probability of landing in the inside shape can be
calculated by finding the area of the inside shape and the area of
the outside shape and writing the results as a fraction. This
activity allows you to manipulate the lengths of the sides and
therefore change the areas. Follow the directions given in the
activity. Use the dots below to change the values of the lengths.
Then, on separate paper, calculate the probability to see if you get
the same answer as the program. Practice with five different
lengths.

Completing this activity should take approximately 30 minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.7.SP.C.7](http://www.corestandards.org/Math/Content/7/SP/C/7)
- [CCSS.ELA-Literacy.RST.6-8.3](http://www.corestandards.org/ELA-Literacy/RST/6-8/3)
- [CCSS.ELA-Literacy.RST.6-8.7](http://www.corestandards.org/ELA-Literacy/RST/6-8/7)
- [CCSS.ELA-Literacy.WHST.6-8.1b](http://www.corestandards.org/ELA-Literacy/WHST/6-8/1/b)
- [CCSS.ELA-Literacy.WHST.6-8.4](http://www.corestandards.org/ELA-Literacy/WHST/6-8/4)
Terms of Use: This work is licensed under a [Creative Commons
Attribution-ShareAlike 3.0 Unported
License](http://creativecommons.org/licenses/by-sa/3.0/).
```

**Did I Get This? Activity: orgLib: “Preview Questions for Test: 7.SP.7 - Worksheet”**Link: orgLib: “Preview Questions for Test: 7.SP.7 - Worksheet” (HTML)

Instructions: Scroll down to the four questions and click on “Consume” beneath them. You will be brought to a new screen where you can type in your answers. After each question you will need to click on “Submit Answer.” When you have all four questions done, you will click on “Submit Test.” At this point, you will be brought to a screen that will show whether your answers are correct.

Completing this activity should take approximately 15 minutes.

Standards Addressed (*Common Core*):

**5.2 Samples**
*Have you ever heard a commercial claim “9 out of 10 dentists recommend
this toothpaste”? The claim that 9 out of 10 dentists like the
toothpaste isn’t very meaningful if 9 of the 10 dentists also work for
that toothpaste company. In that case, the sample that was questioned
does not truly represent the entire population of dentists. In this
subunit, we will take a look at samples and see how a well-chosen sample
can represent the population and help make informed decisions.*

**Explanation: CK-12: “Random and Biased Sampling in a Population”**Link: CK-12: “Random and Biased Sampling in a Population” (PDF)

Instructions: Read the entire article on sampling. While reading, please do the following in your notes:- 1. Give three ways to ensure that you have a random sample.
- 2. Share at least two ways you can model data from a survey.
- 3. Use examples 2 and 3 to help you create your own example of using a proportion to find out how many.

Completing this activity should take approximately 30 minutes.

Standards Addressed (*Common Core*): - CCSS.Math.Content.7.SP.A.1 - CCSS.Math.Content.7.SP.A.2 - CCSS.ELA-Literacy.RST.6-8.3 - CCSS.ELA-Literacy.RST.6-8.7 - CCSS.ELA-Literacy.WHST.6-8.1b - CCSS.ELA-Literacy.WHST.6-8.4Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. It is attributed to CK-12 Foundation. The original version can be found here.

**Explanation: CK-12: “Surveys and Samples”**Link: CK-12: “Surveys and Samples” (PDF)

Instructions: Complete the entire lesson by reading the information, watching the 12-minute video, and solving the practice questions. This lesson will help build knowledge of samples, how to interpret the data, and how to design experiments and conduct surveys.

Completing this activity should take approximately 1 hour and 15 minutes.

Standards Addressed (*Common Core*):Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. It is attributed to CK-12 Foundation. The original version can be found here.

**Did I Get This? Activity: orgLib: “Preview Questions for Test: 7.SP.1 - Worksheet”**Link: orgLib: “Preview Questions for Test: 7.SP.1 - Worksheet” (HTML)

Instructions: Scroll down to the four questions and click on “Consume” beneath them. You will be brought to a new screen where you can type in your answers. After each question you will need to click on “Submit Answer.” When you have all four questions done, you will click on “Submit Test.” At this point, you will be brought to a screen that will show whether your answers are correct.

Completing this activity should take approximately 15 minutes.

Standards Addressed (*Common Core*):**Did I Get This? Activity: orgLib: “Preview Questions for Test: 7.SP.2 – Worksheet”**Link: orgLib: “Preview Questions for Test: 7.SP.2 – Worksheet” (HTML)

Instructions: Scroll down to the four questions and click on “Consume” beneath them. You will be brought to a new screen where you can type in your answers. After each question you will need to click on “Submit Answer.” When you have all four questions done, you will click on “Submit Test.” At this point, you will be brought to a screen that will show whether your answers are correct.

Completing this activity should take approximately 15 minutes.

Standards Addressed (*Common Core*):

**5.3 Compare Data Sets**
*Oftentimes we look at one set of data in a graph or table. However,
there are times when we might want to compare two different sets of
data. Maybe Mr. Smith’s math class is in a competition with Ms.
Sanchez’s class. Both classes have a set of data that will need to be
compared to see who wins the competition. This subunit looks at
different ways of comparing multiple sets of data. It starts by looking
at different types of graphs and measures of center and variability.
Then it continues on to discuss multiple sets of data.*

**5.3.1 Mean Deviation**
- **Interactive Lab: GeoGebra: “Calculate Mean Absolute Deviation
(M.A.D.)”**
Link: GeoGebra: “Calculate Mean Absolute Deviation
(M.A.D.)” (HTML)

Instructions: There is a detailed list of the steps that need to be
taken to get the MAD at the bottom of the worksheet. Follow them to
calculate the MAD. Then use the option to show the steps in #1 to
check your work.

Completing this activity should take approximately 15 minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.7.SP.B.3](http://www.corestandards.org/Math/Content/7/SP/B/3)
- [CCSS.Math.Content.7.SP.B.4](http://www.corestandards.org/Math/Content/7/SP/B/4)
Terms of Use: This work is licensed under a [Creative Commons
Attribution-ShareAlike 3.0 Unported
License](http://creativecommons.org/licenses/by-sa/3.0/).
```

**5.3.2 Box and Whisker Plots**
- **Explanation: CK-12: “Box-and-Whisker Plots”**
Link: CK-12: “Box-and-Whisker
Plots” (PDF)

Instructions: Read the lesson on creating a box-and-whisker plot
until you reach the videos from Khan Academy. While reading, take
note of what the following terms mean and where they appear in a
box-and-whisker plot: median, upper quartile, and lower quartile.

Completing this activity should take approximately 15 minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.7.SP.B.3](http://www.corestandards.org/Math/Content/7/SP/B/3)
- [CCSS.Math.Content.7.SP.B.4](http://www.corestandards.org/Math/Content/7/SP/B/4)
- [CCSS.ELA-Literacy.RST.6-8.4](http://www.corestandards.org/ELA-Literacy/RST/6-8/4)
Terms of Use: This resource is licensed under a [Creative Commons
Attribution-NonCommercial-ShareAlike 3.0 Unported
License](http://creativecommons.org/licenses/by-nc-sa/3.0/). The
text is attributed to CK-12 and the video is attributed to Khan
Academy. The original version can be found
[here](http://www.ck12.org/user%3AbXN0b2RlcmxAcGVyaGFtLmsxMi5tbi51cw../book/Mrs.-Stoderl%2527s-Pre-Algebra-book/r20/section/13.4/).
```

**5.3.3 Stem and Leaf Plots**
- **Explanation: CK-12: “Stem-and-Leaf Plots”**
Link: CK-12: “Stem-and-Leaf
Plots” (PDF)

Instructions: Start by reading the example of using data from the
Iditarod in Alaska. Continue reading until you reach the videos.
Take note of the following while reading.

```
- 1. How is the stem different than a leaf?
- 2. How can I write a three-digit number as a stem and leaf?
- 3. What does the key for a stem and leaf plot look like?
- 4. How can I get the mean, median, and mode from the stem and
leaf plot?
Next, watch the video from Khan Academy in order to see a stem and
leaf plot made and why it is important. Finally, using the
information in the reading and the video, answer the questions in
the “Time to Practice” section.
Completing these activities should take approximately 1 hour.
Standards Addressed (*Common Core*):
- [CCSS.Math.Content.7.SP.B.3](http://www.corestandards.org/Math/Content/7/SP/B/3)
- [CCSS.Math.Content.7.SP.B.4](http://www.corestandards.org/Math/Content/7/SP/B/4)
- [CCSS.ELA-Literacy.RST.6-8.2](http://www.corestandards.org/ELA-Literacy/RST/6-8/2)
Terms of Use: This resource is licensed under a [Creative Commons
Attribution-NonCommercial-ShareAlike 3.0 Unported
License](http://creativecommons.org/licenses/by-nc-sa/3.0/). The
text is attributed to CK-12 and the video is attributed to Khan
Academy. The original version can be found
[here](http://www.ck12.org/user%3AbXN0b2RlcmxAcGVyaGFtLmsxMi5tbi51cw../book/Mrs.-Stoderl%2527s-Pre-Algebra-book/r20/section/13.3/).
```

**5.3.4 Comparing Multiple Sets of Data**
- **Explanation: CK-12: “Data Analysis Using Dot Plots, Measures of
Central Tendency, and Interquartile Range”**
Link: CK-12: “Data Analysis Using Dot Plots, Measures of Central
Tendency, and Interquartile
Range” (PDF)

Instructions: Read through the lesson, taking note of how measures
of center (mean, median, mode) and measures of variability (MAD,
interquartile range, range) can be used to compare two sets of
data.

Reading this lesson should take approximately 30 minutes.

Standards Addressed (*Common Core*):

```
- [CCSS.Math.Content.7.SP.B.3](http://www.corestandards.org/Math/Content/7/SP/B/3)
- [CCSS.Math.Content.7.SP.B.4](http://www.corestandards.org/Math/Content/7/SP/B/4)
Terms of Use: This resource is licensed under a [Creative Commons
Attribution-NonCommercial-ShareAlike 3.0 Unported
License](http://creativecommons.org/licenses/by-nc-sa/3.0/). It is
attributed to CK-12 Foundation. The original version can be found
[here](http://www.ck12.org/na/Data-Analysis-Using-Dot-Plots,-Measures-of-Central-Tendency,-and-Interquartile-Range---7.SP.3,4-1/lesson/user:c2ZveDJAb3N3ZWdvLm9yZw../Data-Analysis-Using-Dot-Plots%252C-Measures-of-Central-Tendency%252C-and-Interquartile-Range---7.SP.3%252C4/).
```

**Did I Get This? Activity: orgLib: “Preview Questions for Test: 7.SP.3 - Worksheet”**Link: orgLib: “Preview Questions for Test: 7.SP.3 - Worksheet” (HTML)

Instructions: Scroll down to the four questions and click on “Consume” beneath them. You will be brought to a new screen where you can type in your answers. After each question you will need to click on “Submit Answer.” When you have all four questions done, you will click on “Submit Test.” At this point, you will be brought to a screen that will show whether your answers are correct.

Completing this activity should take approximately 15 minutes.

Standards Addressed (*Common Core*):**Did I Get This? Activity: orgLib: “Preview Questions for Test: 7.SP.4 - Worksheet”**Link: orgLib: “Preview Questions for Test: 7.SP.4 - Worksheet” (HTML)

Instructions: Scroll down to the four questions and click on “Consume” beneath them. You will be brought to a new screen where you can type in your answers. After each question you will need to click on “Submit Answer.” When you have all four questions done, you will click on “Submit Test.” At this point, you will be brought to a screen that will show whether your answers are correct.

Completing this activity should take approximately 15 minutes.

Standards Addressed (*Common Core*):**Checkpoint: Illustrative Mathematics: “College Athletes”**Link: Illustrative Mathematics: “College Athletes” (PDF)

Instructions: Complete parts a though e. You may use a calculator when completing this checkpoint. Then check your work on page 3.

Completing this checkpoint and checking your work should take approximately 1 hour.

Standards Addressed (*Common Core*):Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. It is attributed to Illustrative Mathematics. The original version can be found here.

**Checkpoint: Illustrative Mathematics: “Waiting Times”**Link: Illustrative Mathematics: “Waiting Times” (PDF)

Instructions: Determine the number of boxes of cereal that would need to be purchased in parts A and B. Then scroll to page 2 to check your work.

Completing this checkpoint and checking your work should take approximately 15 minutes.

Standards Addressed (*Common Core*):Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. It is attributed to Illustrative Mathematics. The original version can be found here.

**Final Exam**
- **Final Exam: The Saylor Foundation’s “K12MATH007 Final Exam”**
Link: The Saylor
Foundation’s “K12MATH007
Final
Exam” (HTML)

```
Instructions: Complete this exam.
Note: 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.
```