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

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

SURVEYS Slide 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.

EXAMPLE: ANALYZING A SURVEY Slide 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?

EXAMPLE: ANALYZING A SURVEY Slide Construct a Venn diagram. Let F = football, B = baseball, and H = hockey. H F B 20 Start with like all 3

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

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

EXAMPLE: ANALYZING A SURVEY Slide Construct a Venn diagram. Let F = football, B = baseball, and H = hockey. H F B Subtract total shown from 140 to get

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

CARDINAL NUMBER FORMULA For any two sets A and B, Slide

EXAMPLE: APPLYING THE CARDINAL NUMBER FORMULA Find n(A) if Slide Solution

EXAMPLE: ANALYZING DATA IN A TABLE Slide 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.

EXAMPLE: ANALYZING DATA IN A TABLE Slide Coffee (C) Juice (J) Tea (T) Totals (Y) (M) Over 33 (O) Totals

EXAMPLE: ANALYZING DATA IN A TABLE Slide (C)(C)(J)(J)(T)(T) Totals (Y)(Y) (M)(M) (O)(O) Totals Using the letters in the table, find the number of people in each of the following sets. a) b)

EXAMPLE: ANALYZING DATA IN A TABLE Slide (C)(C)(J)(J)(T)(T) Totals (Y)(Y) (M)(M) (O)(O) Totals a) in both Y and C b) not in O (so Y + M) + those not already counted that are in T = 15. = = 156.