Question

a survey of 65 customers was taken at a bookstore regarding the types of books purchased. the survey found that 38 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 \\(\square\\) customers who purchased mysteries and science fiction, but not romance novels.
(simplify your answer.)

Explanation:

Step1: Identify the number who bought all three

We know 6 bought all three (mysteries, science fiction, romance).

Step2: Subtract from mysteries and science fiction

The number who bought mysteries and science fiction is 17. To find those who bought only mysteries and science fiction (not romance), we subtract those who bought all three: $17 - 6 = 11$.

Answer:

11