SOLUTION: Missy stood in front of AMC theaters in Independence last week and asked 500 people what kind of movies they liked. She found that: 240 liked dramas 137 liked comedies 94 lik

Question 1118878: Missy stood in front of AMC theaters in Independence last week and asked 500 people what kind of movies they liked. She found that:
240 liked dramas
137 liked comedies
94 liked science fiction
67 like dramas and comedies
42 liked dramas and science fiction
47 liked comedies and science fiction
36 liked all three types of movies.
Draw the Venn Diagram and determine the following:
a. How many liked none of these types of movies?
b. How many liked only the dramas?
c. How many liked exactly one of these types of movies?
d. How many liked exactly two of these types of movies?
e. How many liked dramas or comedies?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

36 like all three, so 36 goes in the spot where all three circles overlap. Then since 67 like both Drama and Comedy, but you have already accounted for the 36 that are included in that 67 because they like all three, you have 67 minus 36 = 31 that Drama & Comedy but Not SciFi. Hence 31 goes in the space that is the overlap between the Drama and Comedy circles but does not include any portion of the SciFi circle. A similar analysis shows that 6 people like Drama & SciFi but Not Comedy.

Then, of the 240 people who like drama, you have accounted for 6 + 36 + 31 = 73 people who also like one, the other, or both of the other types of movies. This leaves 240 - 73 = 167 people who like Drama ONLY. So 167 goes in the portion of the Drama circle that does not overlap either of the other circles.

Using the same type of analysis, fill in the rest of the spaces inside the circles. When you have all of the spaces that are inside circles filled out, add all of the numbers that are in all of those spaces. This is the number of people who liked ANY kind of the three types of movies at all, and 500 minus this number is the number of people who don't like any of the three types of movies.

John

My calculator said it, I believe it, that settles it

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