when you don’t know the value in the intersection A survey of 24 students was carried out to see which type of movies they like to watch. 16 students liked action movies, 12 students liked romantic comedies and 2 students liked neither. (i) Draw a Venn diagram to show this information. (ii) How many students liked both action movies and romantic comedies?
Solution (i)
When you don’t know the intersection, start from the outside.
(ii)
Practice questions 24.2
1. Twenty students in a group of 40 study Science. Eleven students study Art. Five students study both. (i) Draw a Venn diagram to represent this information. (ii) How many students study Science only? (iii) How many students study neither subject? (iv) Find the number of students who have chosen to study at least one of the two subjects. (v)
If a student is choosen at random, what is the probability they don’t study Science?
2. In a group of 24 friends, 11 play golf and 9 of them play basketball. Two play both sports. (i) Represent the data above in a Venn diagram. (ii) How many people play golf only? (iii) How many people, in total, do not play basketball?
(iv) If a person was randomly selected from this group, what is the probability they would play neither sport? Give your answer as a percentage of the the total amount of people.