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Section 2-4

Section 2-4. Surveys and Cardinal Numbers. Surveys and Cardinal Numbers. Surveys Cardinal Number Formula. Surveys.

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Section 2-4

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  1. Section 2-4 • Surveys and Cardinal Numbers

  2. Surveys and Cardinal Numbers • Surveys • Cardinal Number Formula

  3. Surveys Problems involving sets of people (or other objects) sometimes require analyzing known information about certain subsets to obtain cardinal numbers of other subsets. The “known information” is often obtained by administering a survey.

  4. Example: Analyzing a Survey Suppose that a group of 140 people were questioned about particular sports that they watch regularly and the following information was produced. 93 like football 40 like football and baseball 70 like baseball 25 like baseball and hockey 40 like hockey 28 like football and hockey 20 like all three a) How many people like only football? b) How many people don’t like any of the sports?

  5. B F 20 H Example: Analyzing a Survey Construct a Venn diagram. Let F = football, B = baseball, and H = hockey. Start with like all 3

  6. B F 20 Subtract to get 20 8 5 H Example: Analyzing a Survey Construct a Venn diagram. Let F = football, B = baseball, and H = hockey.

  7. B F 20 25 Subtract to get 45 20 8 5 7 H Example: Analyzing a Survey Construct a Venn diagram. Let F = football, B = baseball, and H = hockey.

  8. B F 20 25 45 20 8 5 7 10 H Example: Analyzing a Survey Construct a Venn diagram. Let F = football, B = baseball, and H = hockey. Subtract total shown from 140 to get

  9. Analyzing a Survey • Solution • (from the Venn diagram) • a) 45 like only football • 10 do not like any sports

  10. Cardinal Number Formula For any two sets A and B,

  11. Example: Applying the Cardinal Number Formula Find n(A) if Solution

  12. Example: Analyzing Data in a Table On a given day, breakfast patrons were categorized according to age and preferred beverage. The results are summarized on the next slide. There will be questions to follow.

  13. Example: Analyzing Data in a Table

  14. Example: Analyzing Data in a Table Using the letters in the table, find the number of people in each of the following sets. a) b)

  15. Example: Analyzing Data in a Table = 15. • in both YandC b) not in O (so Y+ M) + those not already counted that are in T = 55 + 77 + 24 = 156.

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