A survey of 70 Customers was taken at a bookstore regarding the types of books purchased. The survey found that 42 customers purchased mysteries, 34 purchased science fiction, 24 purchased romance novels, 18 purchased mysteries and science fiction, 12 purchased mysteries and romance novels, 9 purchased science fiction and romance novels, and 3 purchased all three types of books..........  a). How many customers purchased only Mysteries. b).  How many pur

chased mysteries and science fiction, but not romance novels. c).  How many purchased mysteries or science. d).  How many purchased mysteries or science fiction, but not romance novels. e).  How many purchased exactly two types of books......

You need a VENN diagram to answer this question with circles for mysteries, sci fi and romance.

They will all intersect and there will be a triple intersection in the middle with "3"

Then you work back to the double intersections... subtracting 3 from each of those.

To get you started I have 3 in the triple intersection 9 in the M and R intersection, 15 in the M and SF intersection and 6 in the R and SF intersection. Now.. you need to fill in the big circles. For example in the intersections for Mysteries I have 9 + 3 + 6 = 18
I have to subtract that from 42 to get those who just purchased mysteries. You have to do that for the other two circles. Now, add up all the numbers and see if they add to 70, if they don't you have some people outside the diagram that purchased none of them. Once you have your diagram, you can answer your questions and someone here will check your answers.

To solve this problem step-by-step:

a) To find the number of customers who purchased only mysteries, we need to subtract the customers who purchased mysteries and other genres from the total number of customers who purchased mysteries.

Number of customers who purchased only mysteries = Number of customers who purchased mysteries - Number of customers who purchased mysteries and science fiction - Number of customers who purchased mysteries and romance novels + Number of customers who purchased all three types of books

Number of customers who purchased only mysteries = 42 - 18 - 12 + 3
= 15

b) To find the number of customers who purchased mysteries and science fiction, but not romance novels, we need to subtract the customers who purchased all three types of books from the total number of customers who purchased mysteries and science fiction.

Number of customers who purchased mysteries and science fiction, but not romance novels = Number of customers who purchased mysteries and science fiction - Number of customers who purchased all three types of books

Number of customers who purchased mysteries and science fiction, but not romance novels = 18 - 3
= 15

c) To find the number of customers who purchased mysteries or science, we need to count the customers who purchased only mysteries, only science fiction, and both mysteries and science fiction separately and add them together.

Number of customers who purchased mysteries or science = Number of customers who purchased only mysteries + Number of customers who purchased only science fiction + Number of customers who purchased both mysteries and science fiction

Number of customers who purchased mysteries or science = 15 + (34 - 18 - 3) + (18 - 3)
= 15 + 13 + 15
= 43

d) To find the number of customers who purchased mysteries or science fiction, but not romance novels, we need to subtract the customers who purchased all three types of books from the total number of customers who purchased mysteries, science fiction, or both genres.

Number of customers who purchased mysteries or science fiction, but not romance novels = Number of customers who purchased mysteries or science fiction - Number of customers who purchased all three types of books

Number of customers who purchased mysteries or science fiction, but not romance novels = (42 + 34 - 18 - 3) - 3
= 55 - 3
= 52

e) To find the number of customers who purchased exactly two types of books, we add the customers who purchased mysteries and science fiction, mysteries and romance novels, science fiction and romance novels.

Number of customers who purchased exactly two types of books = Number of customers who purchased mysteries and science fiction + Number of customers who purchased mysteries and romance novels + Number of customers who purchased science fiction and romance novels

Number of customers who purchased exactly two types of books = 18 + 12 + 9
= 39

So, the answers are:
a) 15 customers purchased only mysteries.
b) 15 customers purchased mysteries and science fiction, but not romance novels.
c) 43 customers purchased mysteries or science.
d) 52 customers purchased mysteries or science fiction, but not romance novels.
e) 39 customers purchased exactly two types of books.

To find the answers to these questions, we can use a Venn diagram.

First, let's draw a Venn diagram with three circles representing the types of books: mysteries, science fiction, and romance novels.

a) To find how many customers purchased only mysteries, we need to count the number of customers in the mysteries circle who are not in any other circles. From the given information, we know that 18 customers purchased mysteries and science fiction, 12 purchased mysteries and romance novels, and 3 purchased all three types of books. So, 18 + 12 + 3 = 33 customers purchased mysteries in total. Since the total number of customers surveyed is 70, subtracting 33 from 70 gives us the number of customers who purchased only mysteries: 70 - 33 = 37 customers.

b) To find how many customers purchased mysteries and science fiction but not romance novels, we need to look at the intersection of the mysteries and science fiction circles. From the given information, we know that 18 customers purchased mysteries and science fiction. To exclude those who also purchased romance novels, we subtract the 3 customers who purchased all three types of books. So, 18 - 3 = 15 customers purchased mysteries and science fiction but not romance novels.

c) To find how many customers purchased mysteries or science, we need to count the total number of customers in the mysteries and science fiction circles together. From the given information, we know that 18 customers purchased mysteries and science fiction, but we don't know how many customers purchased only science fiction. So, we need to calculate the number of customers who purchased only science fiction. To do this, subtract the 15 customers who purchased mysteries and science fiction but not romance novels from the total number of customers who purchased science fiction: 34 - 15 = 19. Finally, add the 18 customers who purchased mysteries and science fiction to the 19 customers who purchased only science fiction: 18 + 19 = 37 customers who purchased mysteries or science.

d) To find how many customers purchased mysteries or science fiction but not romance novels, we need to count the total number of customers in the mysteries and science fiction circles but exclude the overlap with the romance novels circle. From the given information, we know that 18 customers purchased mysteries and science fiction, and 9 purchased science fiction and romance novels. We also know that 3 customers purchased all three types of books. To find the number of customers who purchased mysteries or science fiction but not romance novels, we add the customers who purchased only mysteries (37) to the customers who purchased only science fiction (19), and subtract the customers who purchased all three types of books (3): 37 + 19 - 3 = 53 customers.

e) To find the number of customers who purchased exactly two types of books, we need to count the total number of customers in the overlapping regions of the Venn diagram. From the given information, we know that 3 customers purchased all three types of books. To find the number of customers who purchased exactly two types, we add the number of customers who purchased mysteries and science fiction (18) to the number of customers who purchased mysteries and romance novels (12) to the number of customers who purchased science fiction and romance novels (9), and subtract the customers who purchased all three types (3): 18 + 12 + 9 - 3 = 36 customers.