**Unit 7: Probability and Statistics**
*Probability and statistics are the final mathematical topics important
to master in order to do well on the SAT. These are not complicated
topics at all; you just need to know how to do them! This unit will
show you how to easily answer any SAT question on probability or
possible permutations of an event, as well as how to determine the basic
descriptive statistics of a data set.*

**Unit 7 Time Advisory**

This unit should take approximately 3.75 hours to complete.

☐ Subunit 7.1: 0.5 hours

☐ Subunit 7.2: 0.5 hours

☐ Subunit 7.4: 0.75 hours

☐ Subunit 7.5: 2 hours

**Unit7 Learning Outcomes**

Upon successful completion of this unit, the student will be able to:
- Calculate the probability of an event.
- Calculate the probability of two or more events occurring in
succession.
- Calculate the number of ways an event can occur.
- Calculate basic statistical values.

**7.1 Probability**
- **Reading: ErikTheRed.com: Erik Jacobsen’s “SAT Math Facts and
Formulas”**
Link: ErikTheRed.com: Erik Jacobsen’s “SAT Math Facts and
Formulas” (PDF)

```
Instructions: Please click on the link above and select the link to
the “SAT Math Facts and Formulas” PDF. Read the section entitled
“Averages, Counting, Statistics, Probability” (page 2). For all of
these formulas, you should try substituting actual numbers for the
variables, so you can see how the formulas would work for an actual
problem. This resource will cover the topics outlined in subunits
7.1-7.3, as well as any inclusive sub-subunits.
Reading these sections, taking notes, and practicing the formulas
should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
```

**7.1.1 One Event**
*Note: This topic is covered by the resource assigned below subunit
7.1. As an example, use a scenario where you have 4 yellow balls, 3 red
balls, 5 blue balls, and 1 black ball inside a hat. What is the
likelihood that you would pick each of the colors on your first draw?*

**7.1.2 Sequence of Events**
*Note: This topic is covered by the resource assigned below subunit
7.1. Multiply the probability of the first event by the probability of
the second event, third event, etc.*

**7.2 Permutations and Combinations**
- **Web Media: Khan Academy’s “Introduction to Permutations” and
“Introduction to Combinations”**
Link: Khan Academy’s “Introduction to
Permutations” (YouTube)
and “Introduction to
Combinations”
(YouTube)

```
Instructions: Please click on the links above and watch these
videos for an explanation of permutations and combinations as well
as how to approach these problems.
Watching these videos and pausing to take notes should take
approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
```

**7.3 Mean, Median, and Mode**
*Note: This topic is covered by the reading assigned below subunit 7.1.
Note that what the worksheet refers to as the “average” is the same as
the mean.*

**7.4 Probability and Statistics Practice Problems**
- **Assignment: cK-12: Jason Shah’s “SAT Prep - Math Questions” and
“SAT Prep - Math Questions with Explanations”**
Link: cK-12: Jason Shah’s “SAT Prep - Math
Questions” (HTML) and
“SAT Prep - Math Questions with
Explanations” (HTML)

```
Instructions: Please click on the first link above for “Math
Questions” and complete questions 9 and 10 to apply your knowledge
and to prepare for probability and statistics questions on the
SAT.
Once you have completed the questions, please click on the second
link above for “Math Questions with Explanations” and review the
correct answers for questions 9 and 10. For any questions you
missed, read and review the provided explanations until the correct
answer makes sense to you. You may want to look back at the
previous sections in this unit for help. Once you have studied the
correct answer, think about how you will approach a similar problem
in the future and will avoid making a similar mistake.
Completing this assignment should take less than 15 minutes.
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
```

**Assignment: cK-12: Jason Shah’s “SAT Prep II - Math Questions” and “SAT Prep II - Math Questions with Explanations”**Link: cK-12: Jason Shah’s “SAT Prep II - Math Questions” (HTML) and “SAT Prep II - Math Questions with Explanations” (HTML)Instructions: Please click on the first link above for “Math Questions” and complete questions 9 and 10 to apply your knowledge and to prepare for probability and statistics questions on the SAT.

Once you have completed the questions, please click on the second link above for “Math Questions with Explanations” and review the correct answers for questions 9 and 10. For any questions you missed, read and review the provided explanations until the correct answer makes sense to you. You may want to look back at the previous sections in this unit for help. Once you have studied the correct answer, think about how you will approach a similar problem in the future and will avoid making a similar mistake.

Completing this assignment should take less than 15 minutes.

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

**Assignment: cK-12: Jason Shah’s “SAT Prep III - Math Questions” and “SAT Prep III - Math Questions with Explanations”**Link: cK-12: Jason Shah’s “SAT Prep III - Math Questions” (HTML) and “SAT Prep III - Math Questions with Explanations” (HTML)Instructions: Please click on the first link above for “Math Questions” and complete questions 9 and 10 to apply your knowledge and to prepare for probability and statistics questions on the SAT.

Once you have completed the questions, please click on the second link above for “Math Questions with Explanations” and review the correct answers for questions 9 and 10. For any questions you missed, read and review the provided explanations until the correct answer makes sense to you. You may want to look back at the previous sections in this unit for help. Once you have studied the correct answer, think about how you will approach a similar problem in the future and will avoid making a similar mistake.

Completing this assignment should take less than 15 minutes.

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

**7.5 Timed Practice for the Math Section**
- **Assignment: College Board’s “SAT Preparation Booklet 2007-08”**
Link: College Board’s “SAT Preparation Booklet
2007-08” (PDF)

```
Instructions: Since you have now finished your review of the
content for the math section, use the math sections (2, 5, and 8) of
this practice test for timed practice. Take note of the time limits
indicated at the beginning of the section, set a timer, and see how
well you can do within that time. Then review your answers with the
key on page 84.
For any questions you answered incorrectly, take a moment to look
back and try to understand how you were led astray. Think about how
to avoid the same mistake in the future. Look back at any material
you need to review.
Completing this assignment should take approximately 2 hours.
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
```