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### Course: Digital SAT Math > Unit 3

Lesson 8: Probability and relative frequency: foundations# Probability and relative frequency | Lesson

A guide to probability and relative frequency on the digital SAT

## What are probability and relative frequency problems?

The SAT will ask you to calculate probabilities and relative frequencies using data from

**two-way frequency tables**.Two-way frequency tables include two qualitative variables, one represented by rows and the other represented by columns. For example, the table below summarizes the concert attendance of students in Dr. Romelle and Dr. Yukevich's classes. The two variables are class and concert attendance.

Attended concert | Did not attend concert | Total | |
---|---|---|---|

Dr. Romelle's class | |||

Dr. Yukevich's class | |||

Total |

In this lesson, we'll learn to:

- Read two-way frequency tables
- Use two-way frequency tables to calculate probabilities and relative frequencies
- Use probabilities and relative frequencies to find missing values

**You can learn anything. Let's do this!**

## How do I read two-way frequency tables?

The biggest challenge of table data problems is understanding what the question is asking for. Let's describe some of the values in the table below.

Attended concert | Did not attend concert | Total | |
---|---|---|---|

Dr. Romelle's class | |||

Dr. Yukevich's class | |||

Total |

The number $17$ is in the row "Dr. Romelle's class" and the column "attended concert". We can make a few similar statements using the number $17$ :

students both attended the concert and are from Dr. Romelle's class.$17$ students from Dr. Romelle's class attended the concert.$17$ of the students who attended the concert are from Dr. Romelle's class.$17$

The number $40$ is the total for the column "attended concert". This means $40$ students (from both Dr. Romelle and Dr. Yukevich's classes) attended the concert.

Similarly, the number $33$ is the total for the row "Dr. Yukevich's class". This means there are $33$ students in Dr. Yukevich's class (some attended the concert, some did not).

The number $64$ in the lower right corner is total number of students for

*all*categories.### Try it!

## How do I calculate probabilities and relative frequencies using two-way frequency tables?

Once we correctly identify the values we're looking for in a problem, the rest of the problem is basically dividing two values to find a fraction, percentage, or probability.

**Note:**While probabilities and relative frequencies are different concepts, we perform the same calculations for them.

**Let's use the table below for some example calculations!**

Attended concert | Did not attend concert | Total | |
---|---|---|---|

Dr. Romelle's class | |||

Dr. Yukevich's class | |||

Total |

What fraction of Dr. Romelle's class did not attend the concert?

What percent of students from both classes attended the concert?

If a student from both classes is selected at random, what is the probability that the student is from Dr. Yukevich's class and attended the concert?

### Try it!

## How do I find missing values in a table?

**Note:**missing value questions appear very rarely on the SAT.

Just as we can calculate a probability or relative frequency using the values in two-way frequency tables, we can calculate missing values in a table when given a probability or relative frequency.

Some two-way frequency tables do not provide the totals for us. For these tables, it's helpful to add a row and a column for the totals.

**Let's look at another example using the students in Dr. Romelle and Dr. Yukevich's classes.**

Plays an instrument | Does not play an instrument | Total | |
---|---|---|---|

Dr. Romelle's class | |||

Dr. Yukevich's class | |||

Total |

If $\frac{3}{4}$ of the students in the two classes play an instrument, how many students in Dr. Yukevich's class play an instrument?

### Try it!

## Your turn!

## Want to join the conversation?

- I love checking the comments after finishing every lesson 😂😂(349 votes)
- wallah, same😂(46 votes)

- whos preparing for SAT december?(49 votes)
- me. my current highscore is 1160 can i make it to 1400 by december??(23 votes)

- who is giving october SAT?(31 votes)
- I'm writing the october sat(5 votes)

- pretty easy guys(30 votes)
- why is the answer for the fraction question 7/18 instead of 7/25(24 votes)
- THe queston is: What fraction of classmates who do not own a skateboard also do not own a bike?

whenever you see question asked for a fraction, Easiest way is devide question for the fraction they are asking for.

For example they are asking for a fraction in the above question.

So We need to devide the question

Devide= Who do not own a skateboard / Do not own a bike

so Fraction is 7/18

It's a tricky way to answer these types of question.(11 votes)

- I feel hard to comprehend the last one "Rhesus factor".(16 votes)
- 3 (probability of O) is equal to half.

In probability, The total is always equal to 1.

The total here is six (3 being half)

So that means the total of the others is also 3.

2 are one each.

one left(12 votes)

- Who's preparing for march DSAT??(18 votes)
- me, redoing it(4 votes)

- why are box plots and leaf plots not in the lessons?(14 votes)
- for last question:

3/5+x=1/2

x=1(10 votes) - Those who are finding difficulties to answer the fraction asked questions-

The queston is: What fraction of classmates who do not own a skateboard also do not own a bike?

whenever you see question asked for a fraction, Easiest way is devide question for the fraction they are asking for.

For example they are asking for a fraction in the above question.

So We need to devide the question

Devide= Who do not own a skateboard / Do not own a bike

so Fraction is 7/18

It's a tricky way to answer these types of question.(9 votes)