### 2.4 Survey Problems Objectives:

```Section 4
Survey Problems
Objectives:
• Label sets in Venn diagrams with various
names
• Use Venn diagrams to solve survey
problems
• Understand how to handle contradictory
information in survey problems
Naming Venn Diagrams
r4  B  A
r1   A
B 
We use set notation to name regions of a
Venn diagram.
Naming Venn Diagrams cont.
Example:
Name r2.
r2  A
B
C
Survey Problems
• When we collect and organize data into sets,
we may also want to analyze the
information.
• These types of problems are called
survey problems.
• Example:
A television network wants to
determine how many people like to watch
TV on the weekend but prefer not to see
reality shows.
Survey Problems cont.
The television network conducted a market
survey and obtained the following information
on viewing habits.
TV marketing survey cont.
The universal set contains three subsets.
• Condition (a): there are 3 people in W
E
R.
TV marketing survey cont.
• Condition (b): there are 14 people in
W
E.
TV marketing survey cont.
• Condition (c): 18 have not been counted in R
• Condition (d): 8 people want to see weekday
reality shows, so 5 people have not been
counted in W
R.
E.
TV marketing survey cont.
• Condition (e): there are 12 more members in W, 4 more in E, and
14 more in R.
• Condition (h): there are 13 people outside {W, R, E}.
TV marketing survey cont.
• Do not want to see reality shows: 12 + 11 + 4 + 13 = 40
• Prefer to watch TV on weekend: 14 + 18 + 4 + 13 = 49
Solution:
• The number of people who like to watch TV on the weekend
but prefer not to see reality shows is
n( W ’  R ’) = 13 + 4 = 17
• A survey problem may contain contradictory information.
• Example: What web browsers are used by a certain sample
of people?
Condition (a): 212 have not been counted in W.
• Condition (b): 374 have not been counted in I .
•
• Solution:
212 + 374 = 586 use only one of the two
Data in Tabular Form
A company sells Pilates videos and surveys 180
potential customers with the following results.