(a) Find the number of students who do not participate in any of the three activities. (b) Find the number of students who participate in exactly one of the three activities.

Question

A survey on a group of 120 students revealed that 68 watch soccer, 70 participate in social media and 40 listen music. From the students who watch soccer 30 participate also in social media and 20 participate in both other activities. It has also been known that 28 of the students who listen music participate in social media and 32 of the students who listen music watch soccer.

Answer 1

Draw a Venn diagram, a rectangle, then inside put 3 overlapping circles. The overlap of all 3 is in the middle and has 20. The soccer circle overlaps the music with 32, the social media overlaps the music with 28, the social media overlaps the soccer with 30.

The 30 includes the 20 + 10

the 32 includes the 20 + 12

the 28 includes the 20 + 8

the portions of the circles that do not overlap

include 26 for soccer, 0 for music and 32 for social media

add up 26+32+0+10+20+12+8 = 108

120-108 = 12 students who are not involved in any activity

these 12 are not in the circles but outside them

26+32+0 = 58 students involved in only one activity.

this makes a lot more sense if you sketch the Venn diagram and circles