Question

a survey of 65 customers was taken at a bookstore regarding the types of books purchased. the survey found that 39 customers purchased mysteries, 31 purchased science fiction, 24 purchased romance novels, 17 purchased mysteries and science fiction, 13 purchased mysteries and romance novels, 10 purchased science fiction and romance novels, and 6 purchased all three types of books.
a) how many of the customers surveyed purchased only science fiction?
b) how many purchased mysteries and science fiction, but not romance novels?
c) how many purchased mysteries or science fiction?
d) how many purchased mysteries or science fiction, but not romance novels?
e) how many purchased exactly two types of books?

a) there were 10 customers who purchased only science fiction
(simplify your answer.)

b) there were 11 customers who purchased mysteries and science fiction, but not romance novels
(simplify your answer.)

c) there were 53 customers who purchased mysteries or science fiction
(simplify your answer.)

d) there were 36 customers who purchased mysteries or science fiction, but not romance novels
(simplify your answer.)

e) there were \\(\square\\) customers who purchased exactly two types of books.
(simplify your answer.)

Explanation:

Step1: Analyze each two-type purchase

For mysteries and science fiction only: \(17 - 6 = 11\)
For mysteries and romance only: \(13 - 6 = 7\)
For science fiction and romance only: \(10 - 6 = 4\)

Step2: Sum the two-type only counts

Total exactly two types: \(11 + 7 + 4 = 22\)

Answer:

22