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MAT-144 · In-person sections Exam 3 Review · Unit 3
Exam 3 Review · Q2

The addition rule on a two-way table

A grid of counts, and one question: does this ask for a single cell, or for a whole row plus a whole column? The second kind counts one square twice unless you take it back out.

01 Worked Example Video
▸ VIDEO COMING SOON

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

02 Recognize the Question

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

A margin first

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 =
When the overlap is empty

200 people were asked their age group and their one preferred drink.

Under 30: 48 coffee, 22 tea, 30 juice.
30 and over: 62 coffee, 28 tea, 10 juice.

What is the probability a person chosen at random prefers tea or juice? Round to the nearest hundredth.

P =
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.
03 The Rule
and → one inner cell, over the grand total both conditions hold at once
\(P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)\) 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) Assumed the overlap is never zero. When the two events cannot both happen, it is zero and the rule still applies — you just subtract nothing. (3) Never computed the margins. Almost every answer needs a row or column total, and ALEKS does not print them.
04 Practice — Step by Step
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 =
▸ Related Mini Lessons
Q1 Q3
MAT-144 · EXAM 3 REVIEW · Q2 OF 20