Question 2

A group of 100 students is polled to see how many watched three TV shows, Angie, Bobo

and Conway. The results showed that 55 watched Angie, 53 watched Bobo, 55 watched

Conway, 35 watched Angie and Bobo, 28 watched Angie and Conway, 23 watched Bobo and

Conway, and 10 did not watch any of the three. Let A denote the set of students who

watched Angie, and similarly define sets B and C.

(a) Calculate the number of students in each of the eight subsets shown in the Venn diagram. Copy the Venn diagram and enter the number of students in each subset.

(b) Hence find how many students watched:

(i) Angie and Conway, but not Bobo;

(ii) Bobo only;

(iii) only two of the three shows;

(iv) at least two of the shows.