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A food store surveyed 50 of its shoppers as to whether they had purchased bacon or steak during the past week. The results were 30 had purchased bacon, 20 had purchased steak, and 8 had purchased both bacon and steak. A. Draw and label a Venn Diagram to numerically represent this survey. Now, use the Venn Diagram constructed to answer parts b and c. B. How many of these shoppers bought bacon, but not steak? C. How many of these shoppers bought neither of these two meats?

A food store surveyed 50 of its shoppers as to whether they had purchased bacon or steak during the past week. The results were 30 had purchased bacon, 20 had purchased steak, and 8 had purchased both bacon and steak. A. Draw and label a Venn Diagram to numerically represent this survey. Now, use the Venn Diagram constructed to answer parts b and c. B. How many of these shoppers bought bacon, but not steak? C. How many of these shoppers bought neither of these two meats?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Survey Analysis on Meat Purchases Using a Venn Diagram A food store surveyed 50 of its shoppers to determine whether they had purchased bacon or steak during the past week. The results showed that: - 30 shoppers purchased bacon - 20 shoppers purchased steak - 8 shoppers purchased both bacon and steak #### Tasks: **A. Draw and label a Venn Diagram to numerically represent this survey. Now, use the Venn Diagram constructed to answer parts B and C.** **B. How many of these shoppers bought bacon, but not steak?** **C. How many of these shoppers bought neither of these two meats?** **D. Use the Addition Principle for Counting to answer part E.** **E. How many of these shoppers bought bacon or steak?** --- **Explanation of Diagram:** The Venn Diagram will consist of two overlapping circles: - One circle for bacon buyers - One circle for steak buyers - The overlapping area represents shoppers who bought both bacon and steak **Steps to Construct the Diagram:** 1. Draw two overlapping circles. 2. Label one circle as "Bacon" and the other as "Steak." 3. Place the number 8 in the overlapping part of the circles to represent shoppers who bought both bacon and steak. 4. For Bacon-only (Bacon circle excluding the overlap), subtract the overlapping part from the total bacon buyers. (30 - 8 = 22) 5. For Steak-only (Steak circle excluding the overlap), subtract the overlapping part from the total steak buyers. (20 - 8 = 12) 6. The area outside both circles represents shoppers who bought neither. To find this: - Calculate total unique shoppers from the diagram: 22 (Bacon only) + 12 (Steak only) + 8 (Both) = 42 - Subtract this from the total number of shoppers surveyed: 50 - 42 = 8 Thus, the answers to the specific questions based on the Venn Diagram are: - **B:** 22 shoppers bought bacon, but not steak. - **C:** 8 shoppers bought neither bacon nor steak. - **D and E:** Using the Addition Principle: - Number of shoppers who bought bacon or steak = Bacon only + Steak only + Both = 22 + 12 + 8 = 42
Transcribed Image Text:### Survey Analysis on Meat Purchases Using a Venn Diagram A food store surveyed 50 of its shoppers to determine whether they had purchased bacon or steak during the past week. The results showed that: - 30 shoppers purchased bacon - 20 shoppers purchased steak - 8 shoppers purchased both bacon and steak #### Tasks: **A. Draw and label a Venn Diagram to numerically represent this survey. Now, use the Venn Diagram constructed to answer parts B and C.** **B. How many of these shoppers bought bacon, but not steak?** **C. How many of these shoppers bought neither of these two meats?** **D. Use the Addition Principle for Counting to answer part E.** **E. How many of these shoppers bought bacon or steak?** --- **Explanation of Diagram:** The Venn Diagram will consist of two overlapping circles: - One circle for bacon buyers - One circle for steak buyers - The overlapping area represents shoppers who bought both bacon and steak **Steps to Construct the Diagram:** 1. Draw two overlapping circles. 2. Label one circle as "Bacon" and the other as "Steak." 3. Place the number 8 in the overlapping part of the circles to represent shoppers who bought both bacon and steak. 4. For Bacon-only (Bacon circle excluding the overlap), subtract the overlapping part from the total bacon buyers. (30 - 8 = 22) 5. For Steak-only (Steak circle excluding the overlap), subtract the overlapping part from the total steak buyers. (20 - 8 = 12) 6. The area outside both circles represents shoppers who bought neither. To find this: - Calculate total unique shoppers from the diagram: 22 (Bacon only) + 12 (Steak only) + 8 (Both) = 42 - Subtract this from the total number of shoppers surveyed: 50 - 42 = 8 Thus, the answers to the specific questions based on the Venn Diagram are: - **B:** 22 shoppers bought bacon, but not steak. - **C:** 8 shoppers bought neither bacon nor steak. - **D and E:** Using the Addition Principle: - Number of shoppers who bought bacon or steak = Bacon only + Steak only + Both = 22 + 12 + 8 = 42
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