Movies A survey of 350 customers was taken at Regal Cinemas in Austin, Texas, regarding the type of movies customers liked. The following information was determined.

Question

• 196 liked dramas.
• 153 liked comedies.
• 88 liked science fiction.
• 59 liked dramas and comedies.
• 37 liked dramas and science fiction.
• 32 liked comedies and science fiction.
• 21 liked all three types of movies
Of the customers surveyed, how many liked
• a) none of these types of movies?
• b) only dramas?
• c) exactly one of these types of movies?

I do not know how to determne how to get the answers the A, B and C nor how to input it into a Venn Diagram

Answer 1

Draw 3 overlapping circles, D, C and SF.

Way in the middle where all three overlap, put 21

Where only D and C overlap, put 59

Where D has no overlap with others pu 196

etc
now you have to work from the inside out
to figure out how many like each 2 or each 1 exclusively
For example those liking only D and C
are
59-21 = 38
D and SF = 37-21 =16
C and SF = 32-21 = 11
then
those liking D alone = 196 - 38-21-16 =
121
those liking C alone = 153-38-21-11 =
83
those liking SF alone = 88-16-11-21 =
40
NOW do the problem
a
none = 350 - 121-38-21-16-83-11-40 = 20
b
121
c
121+83+40 = 244
Check my arithmetic!!!