Answer:
a) See the attachment for the completed Venn diagram.
b) The number of people who liked to watch television only is 20.
c) The total number of people who took part in the survey was 200.
Explanation:
Draw a Venn diagram with two overlapping circles.
Label one circle "Radio" and the other circle "TV".
Given that 50 people like to listen to the radio but not like to watch television, place the number 50 in the part of the radio circle that does not overlap the TV circle.
Given that 120 people like to listen to the radio, and 50 people like to listen to the radio but not like to watch television, then the number of people who like to listen to the radio and watch tv is:
- Radio & TV = 120 - 50 = 70
Therefore, place the number 70 in the part where the two circles overlap.
Given that 110 people don't like to watch television, and 50 people like to listen to the radio but not like to watch television, then the number of people who don't like to listen to the radio or watch television is:
- Neither radio or TV = 110 - 50 = 60
Therefore, place the number 60 in the area outside the two circles.
Given that 80 people don't like to listen to the radio, and 60 people don't like to listen to the radio or watch television, then the number of people who like to watch the television only is:
Therefore, place the number 20 in the part of the TV circle that does not overlap the radio circle.
Now the Venn diagram has been completed, we can find the total number of people who took part in the survey by adding all the numbers in the Venn diagram:
- Total number of people = 50 + 70 + 20 + 60 = 200
Therefore, there was a total of 200 people who took part in the survey.