Questions: A survey was conducted where people were asked whether they have a preference for cats, dogs, birds, or none at all. Use the Venn Diagram below, which summarizes the results of the survey, to answer the following questions. Each number in the diagram represents the count within the smallest enclosed region that contains the number. a) How many people preferred cats, but not dogs? b) How many people preferred birds and dogs? c) How many people preferred cats? 10 d) How many people were surveyed total?

A survey was conducted where people were asked whether they have a preference for cats, dogs, birds, or none at all. Use the Venn Diagram below, which summarizes the results of the survey, to answer the following questions. Each number in the diagram represents the count within the smallest enclosed region that contains the number.

a) How many people preferred cats, but not dogs?

b) How many people preferred birds and dogs?

c) How many people preferred cats? 10

d) How many people were surveyed total?

Transcript text: A survey was conducted where people were asked whether they have a preference for cats, dogs, birds, or none at all. Use the Venn Diagram below, which summarizes the results of the survey, to answer the following questions. Each number in the diagram represents the count within the smallest enclosed region that contains the number. a) How many people preferred cats, but not dogs? $\square$ b) How many people preferred birds and dogs? $\square$ $\times$ c) How many people preferred cats? 10 $10 \times$ d) How many people were surveyed total? $\square$

Solution

Solution Steps

Step 1: Identify the regions in the Venn diagram

The Venn diagram shows three circles representing preferences for cats, dogs, and birds.
Each region in the Venn diagram corresponds to a specific combination of preferences.

Step 2: Answer the first question

Question: How many people preferred cats, but not dogs?
Solution: Identify the regions in the Venn diagram that include cats but exclude dogs. These regions are the parts of the "Cats" circle that do not overlap with the "Dogs" circle.
Regions: 10 (only cats) and 7 (cats and birds, but not dogs).
Calculation: 10 + 7 = 17.

Step 3: Answer the second question

Question: How many people preferred birds and dogs?
Solution: Identify the regions in the Venn diagram that include both birds and dogs. These regions are the parts where the "Birds" and "Dogs" circles overlap.
Regions: 5 (birds and dogs, but not cats) and 2 (all three: cats, dogs, and birds).
Calculation: 5 + 2 = 7.