Unit- 1 (Set)- X

SET

(Exercise) 

1. In a survey of a school, 300 students favour to play volleyball, 250 favour to play cricket and 110 favour both of the games. Draw a Venn-diagram and calculate:a. the number of students who play cricket only.
   b. the number of students who play either volleyball or cricket.
2. In a survey, after their SEE, 190 students wanted to be an engineer, 160 wanted to be a doctor and 120 wanted to be both. If 300 students were interviewed, draw a Venn-diagram and find the number of students who wanted to be neither of them. 
3. In a survey of 120 adults, 88 drink cold drinks and 26 drink soft drink. If 17 of them drink neither of them, find out the number of adults who drink both cold and soft drink by using a Venn-diagram. 
4. In a survey of youths, it was found that 85% liked to do something in their village, 60% liked to go to foreign employment. If 5% of them did not like both of them, find:
   a. The percent of youths who like to do something in their village only.
   b. The percent of youths who like foreign employment only.
   c. Draw a Venn–diagram to illustrate the above information. 
5. In a certain exam of grade ten, 75% students got high score in mathematics, 65% students got high score in English. If 6% of them did not get high score in both mathematics and English, then calculate:
   a. the percent of students who got high score in both the subjects.
   b. the total number of students who got high score either in mathematics or in English if 300 students had attended the exam. 
6. In a class of 37 students, the number of students who like marshal arts only is double than the number of students who like athletics only. If 3 students like both and 4 like none of the games, find out how many students like:
   a. Marshal arts
   b. Athletics 
7. A survey was conducted in a group of 100 students of a school. The ratio of students who like mathematics and computer is 3:5. If 30 of them like both subjects and 10 of them like none of them, construct a Venn-diagram to find the number of students who like
   a. Mathematics only
   b. computer only
   c. at most one subject 
8. A survey of students of Bhasker Higher Secondary school shows that 45 students like mathematics and 41 students like science. If 12 students like both the subjects, how many students like either mathematics or science? 
9. A survey carried among 850 villagers shows that 400 of them like to make a water tank, 450 like to make an irrigation plant and 150 like to make both of them. Represent the information in a Venn–diagram and find:
   a. the number of people who like to make a water tank only.
   b.  the number of people who like to make either a water tank or an irrigation plant.
    c.  the number of villagers who like neither of them. 
10. In a survey of some people, 73% like to drink tea, 85% like to drink coffee and 65% like to drink tea as well as coffee. If 210 people like neither tea nor coffee, then find the total number of people taken part in the survey. Also, by a Venn-diagram show how many of them like at least one of the given drink ? 
11. In a survey of 60 students, 23 like to play hockey, 15 like to play basketball and 20 like to play cricket. 7 of them like to play both hockey and basketball, 5 like to play both cricket and basketball, 4 like to play both hockey and cricket and 15 students do not like to play any of these games. Draw a Venn-diagram and find:
    a. how many students like to play hockey, basketball and cricket.
    b. how many students like to play hockey but not cricket.
    c. how many students like to play hockey and cricket but not basketball. 
12. In a survey, 135 students appeared in an examination, 60 students got A+ grade in mathematics, 70 got A+ grade in science and 35 got A+ grade in social studies. 20 of them got A+ grade in mathematics and science, 15 got A+ grade in mathematics and social studies and 10 got A+ in science and social studies. If 5 did not get A+ grade in any of the three subjects, find how many of them got A+ grade in all three subjects. 
13. In a survey of 100 students, 60 like to play football, 48 like to play volleyball and 40 like to play cricket. Similarly 32 of them like to play football and volleyball, 22 like to play football and cricket and 20 like to play both volleyball and cricket. If 5 students like to play all three games, represent the above information in a Venn-diagram and find the number of students who like
    a. none of the games
    b. exactly two of the given games
    c. only of the three games.
14. Among the applicants in a certain vacant post, it is found that 70 are qualified in statistics, 60 are in computer and 50 in English. Also, 30 are qualified in statistics and computer, 20 in computer and English and 25 in English and statistics. If 20 are qualified in all three subjects and each are qualified in at least one subject, then;
    a. represent the information in a Venn-diagram
    b. find the number of applicants who are qualified only in computer.
    c. find total number of applicants. 
15. In a survey of a community, 40% favour Dashain, 45% favour Tihar and 55% favour Chhath. 10% of them favour both Dashain and Tihar, 20% favour Tihar and Chhath and 15% favour Chhath and Dashain. Then;
    a. represent the above information in a Venn – diagram.
    b. calculate the percent of people who favour all three festivals.
    c. if 80 community members have taken part in the survey, find the number of people who favour exactly one festival. 
16. In a survey of tourists who have arrived in Tribhuvan International Airport, 65% want to go to Pokhara, 55% like to go to Lumbini and 40% like to go to Ilam. Also, 30% like to go to Pokhara and Lumbini, 20% like to go to Lumbini and Ilam and 25% like to go to Ilam and Pokhara. If 10% like to go all the three places, then;
    a. represent the above data in a Venn-diagram.
    b. what percent of tourists like to go to exactly two places?
    c. what percent of tourists do not like to go to any of the places?
17. For vacation, some students were asked whether they like to go picnic, hiking or tour. The result was 60% students like to go picnic, 45% hiking, 20% tour, 15% picnic and hiking, 12% hiking and tour, 10% tour and picnic and 7% none of them. If 15 students like all three programs;
    a. represent the above information in a Venn-diagram
    b. how many students are taking part in the programs?
    c. how many students like to go picnic only? 
18. In a survey of 100 people, 65 read daily newspapers, 45 read weekly newspapers, 40 read monthly newspapers, 25 read daily as well as weekly, 20 read daily as well as monthly and 15 read at least one type of newspaper. Find:
    a. how many people read all three types of newspaper.
    b. the number of people who read exactly two newspapers. 
19. In a survey, 50% like cold drinks, 30% like hot drinks and 40% like juice. Likewise, 20% of them like cold and hot drinks, 18% like cold drinks and juice, 12% like hot drinks and juice and 5% like all three drinks. Represent the above information in a Venn–diagram and find percent of people who like:
    a. at least one of the three drinks.
    b. exactly two types of drinks.
    c. exactly one type of drink.
    d. none of the drinks. 
20. Work in the group of students. Each student of every group takes data from one of each class of the school with following opinionnaire:
    a. Like coffee
    b. Like tea
    c. Like green tea
    d. Like coffee and tea
    e. Like tea and green tea
    f. Like green tea and coffee
    g. Like all three of the above
    h. Like none of the above ,
    Then represent the collected data in a Venn-diagram and present it to the classroom.