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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

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Naming Venn Diagrams We use set notation to name regions of a Venn diagram.

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Naming Venn Diagrams cont. Example: Name r 2.

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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.

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Survey Problems cont. The television network conducted a market survey and obtained the following information on viewing habits.

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TV marketing survey cont. The universal set contains three subsets. Condition (a): there are 3 people in

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TV marketing survey cont. Condition (b): there are 14 people in

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TV marketing survey cont. Condition (c): 18 have not been counted in Condition (d): 8 people want to see weekday reality shows, so 5 people have not been counted in

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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}.

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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

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Contradictions in Survey Problems A survey problem may contain contradictory information. Example: What web browsers are used by a certain sample of people?

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Contradictions in Survey Problems cont. 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 browsers which contradicts (d).

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Data in Tabular Form A company sells Pilates videos and surveys 180 potential customers with the following results. Via Access Code = web download of video (a) Find the number of elements in (b) Find the number of elements in a) b)

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