Question 1
In a school, 100 students indicated their interest in the following sports: football, volleyball and hockey. 48 liked football, 42 liked volleyball and 36 liked hockey. 18 liked football only, 6 volleyball only and 4 hockey only. 10 liked all three sports while 12 liked football and volleyball only.
- Illustrate the information on a Venn diagram.
- Find the number of students who liked:
(i) two types of sports only;
(ii) none of the three sports.
Observation
The Chief Examiner reported that a good number of candidates were able to tackle this question satisfactorily. However, some candidates still had difficulty in drawing and interpreting the Venn diagram.
In part(a), they were expected to draw the Venn diagram as shown:
In part (b)(i), they were expected to obtain number of students that liked two types of sports as 12 + 8 + 14 = 34 students.
In part (b)(ii), they did as expected to obtain number of students that liked none of the three sports as 100 – (48 + 6 + 14 + 4) = 100 – 72 = 28 students.