VENN DIAGRAMS. B = {odd numbers greater than 12 and less than 18} A = {composite numbers ranging from 10 to 20} Question 2
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1 Question 1 VENN DIAGRAMS a. Draw a Venn diagram representing the relationship between the following sets. Show the position of all the elements in the Venn diagram. ξ = {integers ranging from 10 to 20} B = {odd numbers greater than 12 and less than 18} A = {composite numbers ranging from 10 to 20} b. Find: i. ii. iii. c. How many numbers are in A only? d. i. Pr ( ii. Question 2 Draw a Venn diagram representing the relationship between the following sets. Show the position of all the elements in the Venn diagram. ξ = {counting numbers up to 10} E = { even number} P = {prime number} (make sure that you list the sets first!!)
2 b. Find: i. ii. iii. iv. c. Find: i. Pr ii. iii. Pr iv. Question 3 8. A sporting club has its members playing different sports, as shown in the Venn diagram. a. How many members: i. play volleyball? ii. are involved in all three activities? b. How many members belong to the sporting club? c. How many members do not i. play tennis ii. walk d. Calculate the probability that a member chosen at random likes: i. Tennis and walking ii. Tennis or walking e. Calculate the probability that a member chosen at random does not like volleyball.
3 Question 4 The following Venn Diagram shows the number of students who play chess and soccer. There are a total of 30 students in the class. x C 12 S 9 5 a. Determine the value of x. b. How many students are there who play chess but not soccer? c. Find the value of : i. ii. iii. d. If a student is chosen randomly from the class, determine the probability that: i. he plays neither chess nor soccer ii. he plays soccer but not chess Question 5 In a survey among year 8 students about how they get to school, the results obtained are shown in the Venn Diagram below. In total, 500 students were interviewed. P = takes public transport regularly C = goes by car regularly P C a. How many students were interviewed in total? b.. How many students regularly do not regularly go either by car or public transport? c. How many students regularly use public transport only? d. Calculate: i. ii.
4 d. How many students regularly use both public transport and a car? e. How many students do not regularly use a car to get to school? Question 6 A survey of a Year 8 class found the numbers of class members who play basketball, cricket and soccer. Use the following Venn diagram to calculate the number of students who: a. were in the class b. play basketball c. play cricket and basketball d. play cricket and basketball but not soccer e. play all three sports f. do not play cricket, basketball or soccer g. do not play cricket h. play cricket or basketball i. play basketball or cricket or soccer.
5 Question 7 A tyre manufacturer conducting a survey of 2200 customers obtained the following results on two tyres: 1390 customers preferred Tyre A, 1084 preferred Tyre B, and 496 preferred both equally. a. Draw a Venn diagram to illustrate the above information. b. Use the Venn diagram to answer the following questions. i. How many customers preferred Tyre A only? ii. iii. How many customers preferred Tyre B only? How many customers preferred neither tyre? Qeustion 8 (CHALLENGE) A group of 40 university lecturers were asked which free-to-air TV stations they watched on a particular evening. Twelve watched SBS, twenty-five watched ABC1 and ten watched neither SBS nor ABC1. a. Show this information on a fully labelled Venn diagram. b. How many watched both SBS and ABC1?
6 Question 9 (CHALLENGE) A survey of 140 fifteen-year-old girls investigated how many read magazines (M), crime novels (C) and science fiction (S). It found: 23 read both magazines and science fiction 21 read both magazines and crime novels 25 read both crime novels and science fiction 15 read all three 40 read magazines only 38 read crime novels only 10 read science fiction only. Show this information on a fully labelled Venn diagram. a. How many girls read magazines? b. How many girls read only crime? c. How many girls read science fiction? d. How many girls read none of these three?
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