2.5djj.notebook
October 01, 2009
Sect. 2.5: Surveys and Cardinal Numbers Objectives 1­ 2
Venn diagrams are used to visualize the results of a survey. Text ex.1: In a campus survey, students were asked 2 questions:
Would you be willing to donate blood?
Would you be willing to help serve a free breakfast to blood donors?
Set A = willing to donate blood Set B = willing to serve breakfast
U
A
B
370 120 220
290
How many students are:
a. willing to donate blood?
_____
b. willing to serve breakfast? _____
c. willing to donate blood and serve breakfast? _____
d. willing to donate blood or serve breakfast?
_____
e. willing to donate blood, but not serve breakfast _____
f. willing to serve breakfast, but not donate blood? _____
g. neither willing to donate blood nor serve breakfast? _____
h. surveyed? _____
Sep 15­6:15 AM
1
2.5djj.notebook
October 01, 2009
Venn diagrams are used to solve problems involving surveys. Generally, start with the intersection of all the sets and work outward.
ex. There were 20 people in a diner. Fifteen had hamburgers, twelve had french fries, and ten had both. U
H
F
How many had neither?
________
How many had hamburgers or french fries?
________
How many had hamburgers, but not french fries? ________
Sep 15­6:17 AM
2
2.5djj.notebook
October 01, 2009
ex. One hundred residents in a dormitory were surveyed as to whether or not they had a TV, a microwave, or a computer in their room. Here are the results:
64 had a computer
62 had a TV
68 had a microwave
42 had a TV and a computer
44 had a TV and a microwave
40 had a microwave and a computer
26 had a TV, a microwave, and a computer
How many had only a computer?
________
How many had at least one of the items?
________
How many had exactly one of the items?
________
How many had exactly 2 of the items?
________
How many had a TV and a microwave, but not a ________
computer?
How many had a computer or a TV?
________
Use Handout on Surveys. See text ex. 1­ 4.
Sep 15­6:27 AM
3