University:
Glendale Community College
Course:
MAT142 | College Mathematics
Academic year:

2020
Views:

379

Pages:

26
Author:

Ruben Owens

Section 1.7 Applications using Venn Diagrams Homework # 1- 5 1) A group of theater majors were asked whether they were in the Drama club or Music club. The results are summarized in the following Venn diagram. a) Describe what each region in the Venn diagram represents. b) How many students were in only one of the two clubs? c) How many students were the drama club or the music club? d) How many students were surveyed? 2) A group of students were asked what pet they had at home. The results are summarized in the following Venn diagram. a) Describe what each region in the Venn diagram represents. b) How many students had exactly one of the two? c) How many students had at least one of the two? d) How many had cats or dogs? 3) A group of coffee drinkers were asked what the added to their coffee. The results are summarized in the following Venn diagram. a) Describe what each region in the Venn diagram represents. b) How many coffee drinkers didn’t use either cream or sugar? c) How many coffee drinkers used cream or sugar? d) How many coffee drinkers only used one of the two? 4) 40 students were asked what kind of pet they had at home. The results are summarized in the following Venn diagram. a) Describe what each region in the Venn diagram represents. b) How many students had exactly one of the three? c) How many students had cats or dogs? d) How many students had cats or dogs, but not birds? 5) The International School offers French, Spanish and Japanese classes. A group of students was asked which languages they had studied. a) Describe what each region in the Venn diagram represents. b) How many students had studied exactly one of the three? c) How many students studied Spanish or French? d) How many students studied Spanish or French, but not Japanese? Two set Venn diagram (THIS ORDER IS VERY IMPORTANT, FOLLOW IT!) Region (follow this order) II I III IV Total Formula Given number from the problem (NFP) NFP – II NFP - II NFP – (I + II + III) Add the numbers in the first column and make sure they equal the desired total Three set Venn diagram (THIS ORDER IS VERY IMPORTANT, FOLLOW IT!) Region (follow this order) V IV II VI I III VII VIII Total Formula Given number from the problem (NFP) NFP – V NFP - V NFP - V NFP – (II + IV + V) NFP – (II + V + VI) NFP – (IV + V + VI) NFP – (I+II+III+IV+V+VI+VII) Add the numbers in the first column and make sure they equal the desired total Homework # 6 – 21 6) 120 coffee drinkers were asked whether they used cream or sugar in their coffee. The summary of the survey was as follows: 55 use sugar 36 use cream 16 use both a) Create a Venn diagram to summarize the information. b) How many used cream in their coffee? c) How many used sugar? d) How many used sugar but not cream? e) How many used cream but not sugar? f) How many used cream and sugar? g) How many used cream or sugar? 7) A veterinarian surveys 26 of his patrons. He discovers that: 14 have dogs 10 have cats 8 have both cats and dogs. a) Create a Venn diagram to model the information. b) How many patrons had dogs or cats? c) How many patrons had dogs but not cats? d) How many patrons didn’t have either? 8) In a group, 30 persons were asked if they like tea or coffee, of these: 18 like coffee 15 like tea 11 like both coffee and tea. How many like coffee? a) Create a Venn diagram to model the information. b) How many people like coffee or tea? c) How many like coffee but not tea? d) How many patrons didn’t like either? 9) In a survey of 20 students in a class: 10 were liked pineapple juice 15 were liked of orange juice 7 liked to have both a) Create a Venn diagram to model the information. b) How many people like pineapple juice or orange juice? c) How many like orange juice but not pineapple juice? d) How many patrons didn’t like either? 10) In a survey of 120 people, Sam found that: 70 people liked product A 80 liked product B 50 people liked both a) Create a Venn diagram to model the information. b) How many liked product A or B c) How many liked product A but not B d) How many didn’t like either? 11) A gym is thinking about adding more cardio equipment for its members. It is considering two types of equipment, treadmills (T) and Stair Masters (S). The gym surveyed a sample of the members and asked which equipment they used in the previous month. Of 150 gym members surveyed it was found that… 102 used the treadmills 71 used the Stair Masters 40 used both types. a) Create a Venn diagram to summarize the information. b) How many did not use either the treadmill or the Stair Master? c) How many used the treadmill but not the Stair Master? d) How many used the Stair Master but not the treadmill? e) How many used at least one of the two? 12) 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 regular  62 liked mint  35 liked both types a) Create a Venn diagram to model the information. b) How many liked only regular? c) How many liked only mint? d) How many liked exactly one of the two (that is they liked one but not the other)? 13) Out of 40 students: 14 are taking Chemistry 29 are taking English 5 are taking both a) Create a Venn diagram to model the information. b) How many students are taking Chemistry, but not English? c) How many are taking Chemistry or English? d) How many are taking exactly one of the two classes? 14) In a class of 50 students 18 are in the chorus 26 are in the band 12 are in both a) Create a Venn diagram to model the information. b) How many were in chorus or band? c) How many were in chorus but not band? d) How many were in exactly one of the two 15) 105 adults were asked whether they had studied French, Spanish or Japanese in school. Here are the results of the survey: 5 are taking all three 9 have studied both Japanese and French 11 have studied both Japanese and Spanish 24 have studied both Spanish and French 52 have studied French 63 have studied Spanish 25 have studied Japanese a) Create a Venn diagram to model the information. b) How many have studied Spanish but not French? c) How many have studied Japanese but not French? d) How many have studied both French and Spanish? e) How many have studied French or Spanish? f) How many have studied both French and Spanish but not Japanese? 16) AAA Travel surveyed 125 potential customers. The following information was gathered. 18 wished to travel to all three destinations 34 wished to travel to Hawaii and Las Vegas 26 wished to travel to Las Vegas and Disney World 23 wished to travel to Hawaii and Disney World 68 wished to travel to Hawaii 53 wished to travel to Las Vegas 47 wished to travel to Disney World a) Create a Venn diagram to summarize the information. b) How many did not wish to travel to any of these destinations? c) How many wished to travel only to Hawaii? d) How many wished to travel to Disney World and Las Vegas, but not to Hawaii? e) How many wished to travel to Disney World or Las Vegas, but not to Hawaii? f) How many wished to only travel to exactly one of these locations? 17) 33 U.S. cities with large populations were surveyed to determine whether they had a professional baseball team, a professional football team, or a professional basketball team. The following information was determined. 5 had all three teams 11 had baseball and football 7 had baseball and basketball 9 had football and basketball 16 had baseball 17 had football 15 had basketball a) Create a Venn diagram to model the information. b) How many cities had only football? c) How many cities had baseball or football? d) How many cities had both baseball and football but not basketball? e) How many had exactly two teams? 18) In a group of 60 students: 2 students play all three 8 play table tennis and swim 6 play cricket and swim 5 play table tennis and cricket 25 play table tennis 16 swim 22 play cricket a) Create a Venn diagram to model the information. b) How many play table tennis and swim and play cricket? c) How many play table tennis but not cricket? d) How many play table tennis and cricket but not do swimming? 19) In a survey of 75 people, Sam found that: 9 liked all the three products 24 people liked both products A and B 20 people liked products C and A 18 people liked product B and C 38 people liked product A 36 liked product B 39 liked product C a) Create a Venn diagram to model the information. b) How many liked product A or B? c) How many liked product both A and B, but not C? d) How many didn’t like any of the three products? 20) 150 students were asked which kind of cell phones they have owned in the past. The results of the survey were as follows: 5 have owned all three 20 have owned both a Galaxy and a flip phone 25 have owned both a Galaxy and an I-phone 15 have owned a flip phone and an I-phone 30 have owned a flip phone 50 have owned an I-phone 40 have owned a Galaxy a) Create a Venn diagram to model the information. b) How many students have not owned any of the three? c) How many have owned a Galaxy or an IPhone? d) How many have only owned exactly one of the three? e) How many have owned exactly two of the three? 21) 100 students were asked which fast food restaurant they have been to this year. The results of the survey were as follows: 5 have been to all three 20 have been to both McDonald’s and Taco Bell 25 have been to both Subway and McDonald’s 15 have been to both Taco Bell and Subway 50 have been to McDonald’s 40 have been to Taco Bell 45 have been to Subway a) Create a Venn diagram to model the information. b) How many did not go to any of the three? c) How many have been to McDonald’s or Taco Bell? d) How many have been to McDonald’s or Taco Bell, but not Subway? e) How many have been to exactly two of the three? Answers: 1a) region I in drama club, not in music club region II in both clubs, region III in music, not in drama region IV not in either club 1b) 16 1c) 31 1d) 43 3a) region I, use cream, do not use sugar region II use both cream and sugar region III use sugar, don’t use cream Region IV don’t use either 3b) 0 3c) 71 3d) 51 5a) region I taking French, not taking Spanish, not taking Japanese region II taking both French and Spanish, not taking Japanese region III taking Spanish, not taking French, not taking Japanese region IV taking both French and Japanese, not taking Spanish region V taking all three region VI taking Spanish and Japanese, not taking French region VII taking Japanese, not taking French, not taking Spanish region VIII not taking any of the three 5b) 23+32+9 = 64 5c) 23+5+4+20+7+32 = 91 5d) 23+32+20=75