1. SECTION 2-4 Surveys and Cardinal Numbers Slide 2-4-1

2. SURVEYS AND CARDINAL NUMBERS Surveys Cardinal Number Formula Slide 2-4-2

3. SURVEYS Slide 2-4-3 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 Slide 2-4-4 Suppose that a group of 140 people were questioned about particular sports that they watch regularly and the following information was produced. 93 like football40 like football and baseball 70 like baseball25 like baseball and hockey 40 like hockey28 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. EXAMPLE: ANALYZING A SURVEY Slide 2-4-5 Construct a Venn diagram. Let F = football, B = baseball, and H = hockey. H F B 20 Start with like all 3

6. EXAMPLE: ANALYZING A SURVEY Slide 2-4-6 Construct a Venn diagram. Let F = football, B = baseball, and H = hockey. H F B 20 58 Subtract to get

7. EXAMPLE: ANALYZING A SURVEY Slide 2-4-7 Construct a Venn diagram. Let F = football, B = baseball, and H = hockey. H F B 20 5 25 8 45 7 Subtract to get

8. EXAMPLE: ANALYZING A SURVEY Slide 2-4-8 Construct a Venn diagram. Let F = football, B = baseball, and H = hockey. H F B 20 5 25 8 45 10 7 Subtract total shown from 140 to get

9. ANALYZING A SURVEY Slide 2-4-9 Solution (from the Venn diagram) a) 45 like only football b)10 do not like any sports

10. CARDINAL NUMBER FORMULA For any two sets A and B, Slide 2-4-10

11. EXAMPLE: APPLYING THE CARDINAL NUMBER FORMULA Find n(A) if Slide 2-4-11 Solution

12. EXAMPLE: ANALYZING DATA IN A TABLE Slide 2-4-12 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 Slide 2-4-13 Coffee (C) Juice (J) Tea (T) Totals 18-25 (Y) 15221855 26-33 (M) 30252277 Over 33 (O) 45222491 Totals 906964223

14. EXAMPLE: ANALYZING DATA IN A TABLE Slide 2-4-14 (C)(C)(J)(J)(T)(T) Totals (Y)(Y)15221855 (M)(M)30252277 (O)(O)45222491 Totals 906964223 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 Slide 2-4-15 (C)(C)(J)(J)(T)(T) Totals (Y)(Y)15221855 (M)(M)30252277 (O)(O)45222491 Totals 906964223 a) in both Y and C b) not in O (so Y + M) + those not already counted that are in T = 15. = 55 + 77 + 24 = 156.