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.
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.
hint: Use Venn diagrams
BTW, what is the question?
To find out how many customers liked at least one type of movie, we need to use the principle of Inclusion-Exclusion.
Step 1: Add up the number of customers who liked each genre individually.
- 196 liked dramas.
- 153 liked comedies.
- 88 liked science fiction.
Total = 196 + 153 + 88 = 437
Step 2: Subtract the customers who liked multiple genres to avoid double-counting.
- 59 liked dramas and comedies.
- 37 liked dramas and science fiction.
- 32 liked comedies and science fiction.
Total = 59 + 37 + 32 = 128
Step 3: Add back the customers who liked all three genres. This is done because they were subtracted twice in Step 2.
- 21 liked all three types of movies.
Total = 128 + 21 = 149
Step 4: Subtract the total obtained in Step 3 from the total obtained in Step 1.
- Total = 437 - 149 = 288
Therefore, 288 customers liked at least one type of movie out of the surveyed 350 customers at Regal Cinemas in Austin, Texas.