Questions: A survey was conducted where people were asked whether they have a preference for cats, dogs, birds, or no preference. The subjects may have preferred more than one animal. The Venn diagram below summarizes the results of the survey, and the values shown in the diagram are the number of people in each subset. a. How many people preferred cats, but not dogs? 21 b. How many people preferred both birds and dogs, but not cats? 6 c. How many total people preferred cats? 32 d. How many total people were surveyed? Remember to include those that chose no preference. 59

A survey was conducted where people were asked whether they have a preference for cats, dogs, birds, or no preference. The subjects may have preferred more than one animal. The Venn diagram below summarizes the results of the survey, and the values shown in the diagram are the number of people in each subset. a. How many people preferred cats, but not dogs? 21 b. How many people preferred both birds and dogs, but not cats? 6 c. How many total people preferred cats? 32 d. How many total people were surveyed? Remember to include those that chose no preference. 59
Transcript text: A survey was conducted where people were asked whether they have a preference for cats, dogs, birds, or no preference. The subjects may have preferred more than one animal. The Venn diagram below summarizes the results of the survey, and the values shown in the diagram are the number of people in each subset. a. How many people preferred cats, but not dogs? $\square$ 21 b. How many people preferred both birds and dogs, but not cats? $\square$ 6 c. How many total people preferred cats? $\square$ 32 d. How many total people were surveyed? Remember to include those that chose no preference. $\square$ 59
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Solution

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Solution Steps

Step 1: People who preferred cats but not dogs

The number of people who preferred cats but not dogs is the sum of the number of people who preferred only cats and the number of people who preferred cats and birds but not dogs. Only cats: 14 Cats and birds but not dogs: 7 Total = 14 + 7 = 21

Step 2: People who preferred both birds and dogs but not cats

The number of people who preferred both birds and dogs but not cats is given by the intersection of the birds and dogs circles, excluding the intersection with the cats circle. This value is given as 6 in the Venn diagram.

Step 3: Total number of people who preferred cats

The total number of people who preferred cats is the sum of all numbers within the cat circle: Only cats: 14 Cats and dogs but not birds: 8 Cats and birds but not dogs: 7 Cats, dogs, and birds: 3 Total = 14 + 8 + 7 + 3 = 32

Final Answer

a. \(\boxed{21}\) b. \(\boxed{6}\) c. \(\boxed{32}\)

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