Sets
4 marks · HardIn a class of 30 students, the universal set U consists of all the students. Let set M be the students who play music (18 students), set S be the students who play sports (15 students), and 8 students play both music and sports.
How many students play only music?
How many students play neither music nor sports?
Represent this information in a Venn diagram. Clearly label all sets and indicate the number of students in each region.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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(a) 10
(b) 5
(c) Venn diagram with Music, Sports circles; 10 (only music), 7 (only sports), 8 (both), 5 (neither) · must show Two intersecting circles labelled M and S inside universal set U, ‘10’ in only M region, ‘7’ in only S region, ‘8’ in the intersection, ‘5’ outside both
Common mistakes: Failing to subtract intersection from totals; Not identifying those in neither set
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · States or calculates number who play only music: 18 - 8 = 10
M2 (b) · 1 mark · Identifies or calculates number who play only sports: 15 - 8 = 7
A1 (b) · 1 mark · Correctly finds number who play neither: 30 - (10 + 7 + 8) = 5 (follow-through)
B1 (c) · 1 mark · Correct Venn diagram with all numbers placed and labelled correctly (follow-through)
Worked solution
a) Number who play only music = total in M - both = 18 - 8 = 10
b) Number who play only sports = 15 - 8 = 7
Total playing at least one: 10 (only music) + 7 (only sports) + 8 (both) = 25
Number who play neither = 30 - 25 = 5