### Slide 1

```Survey Problems
MATH 102
Contemporary Math
S. Rook
Overview
• Section 2.4 in the textbook:
– Survey problems
Survey Problems
Survey Problems
• Essentially we are using previous set
techniques to solve word problems involving
surveys, polls, and reports
– Cardinal number is an important concept
• Drawing a Venn Diagram is invaluable when
solving a survey problem
• MUST practice to master!
Survey Problems (Example)
Ex 1: Find the number of elements in the
desired sets using the given information:
a) n A  B  25, n A  B  7, n A'B  11 ; n(A), n(B)
nB  C   4, nC  B   9, n A  B  C   3, nB  C   22,
b) n A  C   7, n A  B   7, n A  C   5
n(A), n(B), n(C)
Survey Problems (Example)
Ex 2: See exercise 44 on page 71 of the
textbook.
Survey Problems (Example)
Ex 3: Consider the following table representing voting
information on a proposition in the last school election.
a)
c)
Freshmen
(F)
Sophmores
(So)
Juniors
(J)
Seniors
(Sr)
Total
Yes (Y)
700
300
50
15
1065
No (N)
200
100
175
100
575
Did not Vote
(DNV)
100
100
25
10
235
Total
1000
500
250
125
1875
nF  N 
nSo  Y 
b) nDNV  J  Sr
d) nJ '  Sr  N  '
Survey Problems (Example)
Ex 4: Suppose a Nielsen ratings report states the
following information: 6 million people
watched the season finale of NCIS, 3 million
people watches the season finale of Burn
Notice, 1 million watch both, and 8 million
watched only one of the season finales. How
is this information inconsistent?
Summary
• After studying these slides, you should know
how to do the following:
– Solve survey problems using set theory