1 / 7

2.5

2.5. Applications of Sets. Example: Toothpaste Taste Test. A drug company is considering manufacturing a new toothpaste. They are considering two flavors, regular and mint. In a sample of 120 people, it was found that 74 liked the regular, 62 liked the mint, and 35 liked both types .

dubois
Download Presentation

2.5

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 2.5 Applications of Sets

  2. Example: Toothpaste Taste Test • A drug company is considering manufacturing a new toothpaste. They are considering two flavors, regular and mint. • In a sample of 120 people, it was found that 74 liked the regular, 62 liked the mint, and 35 liked both types. • How many liked only the regular flavor? • How many liked either one or the other or both? • How many people did not like either flavor?

  3. Begin by setting up a Venn diagram with sets A (regular flavor) and B (mint flavor). Since some people liked both flavors, the sets will overlap and the number who liked both with be placed in region II. 35 people liked both flavors. Solution

  4. Next, region I will refer to those who liked only the regular and region III will refer to those who liked only the mint. In order to get the number of people in each region, find the difference between all the people who liked each toothpaste and those who liked both. 74 – 35 = 39 62 – 35 = 27 U 39 regular only 27 mint only 35 bot h R egular Mint Solution continued

  5. Solution continued • “One or the other or both” represents the UNION of the two sets. • Therefore, 39 + 27 + 35 = 101 people who liked one or the other or both. • You can also use the following formula: N(A or B) = N(A)+N(B)-N(A and B) N(One or the other or both)=N(regular)+N(mint)-N(both) = 74+62-35 = 101

  6. Solution continued • Take the total number of people in the entire sample (120) and subtract the number who liked one or the other or both (101, from previous step). 120-101=19 people did not like either flavor.

  7. Next Steps • Read Examples 1-3 • Work Problems in text: p. 80: #1-6, all • Do Online homework corresponding to this section • Take Online quiz corresponding to Secs. 2.4 and 2.5

More Related