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MAT-144 · In-person sections Exam 3 Review · Unit 3
Exam 3 Review · Q8

Reading a two-way frequency table

A grid of counts. Every probability on it is one number over another, and the only skill is knowing which two. Two questions on Exam 1 of this unit depend on it.

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A short walkthrough explaining what you need to know and how to solve this question type lands here once it's recorded.

ALEKS randomizes the numbers each attempt, but the question shape stays the same. Here are three example versions you might see.

Shirts and jackets

Of 198 employees, preferences by gender are:

Male: 52 shirt, 93 jacket. Female: 43 shirt, 10 jacket.

One employee is chosen at random. What is the probability they prefer a jacket? Round to the nearest hundredth.

P =
The same table, an or

Same 198 employees. Male: 52 shirt, 93 jacket. Female: 43 shirt, 10 jacket.

What is the probability the employee is female or prefers a jacket? Round to the nearest hundredth.

P =
Relative frequency

195 adults were classified by voter registration and preferred news source.

Registered: 16 television, 17 newspapers, 33 radio, 37 internet.
Not registered: 23 television, 16 newspapers, 34 radio, 19 internet.

What is the relative frequency of adults who are registered and prefer radio? Round to two decimal places.

Heads up: Your ALEKS version will use different numbers. The numbers in the practice below are different too — that way you're exercising the move, not memorizing one answer.
and → one inner cell, over the grand total the two conditions must both hold
\(P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)\) subtract the overlap, or you count it twice
Total the rows and columns first; the margins are where most answers live. An “and” question is a single inner cell. An “or” question adds a whole row to a whole column, which counts the cell where they cross twice, so you subtract it back out once.
Common slips
(1) Added without subtracting the overlap. The row and the column share a cell. (2) Used a row total as the denominator for an “and” question. Plain “and” probabilities go over the grand total. (3) Never computed the margins. Almost every answer needs a row or column total, and ALEKS does not print them.
Margins first

A hundred people at a conference were asked their role and their drink.

THE MARGINS ARE THE TOTALS Coffee Tea Total Student Staff Total 34 21 18 27 55 45 52 48 100 the four inner cells are the data; every amber figure is a total you compute

One person is chosen at random. Round answers to the nearest hundredth.

Step 1

A single cell

What is the probability the person is a student and drinks coffee?
P =
Step 2

A margin

What is the probability the person drinks coffee?
P =
Step 3

The or, with the overlap removed

What is the probability the person is a student or drinks coffee?
P =
Q7 Q9