To solve this problem, we can use a concept called sets and set operations. Let's break down each part of the problem and explain how to get the answer step by step.
A) How many purchased mysteries and science fiction, but not romance?
To answer this question, we need to find the number of customers who purchased both mysteries and science fiction, excluding those who also purchased romance novels.
First, we find the number of customers who purchased mysteries and science fiction together. According to the survey, 13 customers purchased both.
Next, we find the number of customers who purchased mysteries, science fiction, and romance novels. According to the survey, 3 customers purchased all types.
To obtain the number of customers who purchased mysteries and science fiction but not romance, we subtract the number of customers who purchased all types from the number of customers who purchased both mysteries and science fiction: 13 - 3 = 10.
Therefore, 10 customers purchased mysteries and science fiction, but not romance.
B) How many purchased mysteries or science fiction?
To find the number of customers who purchased mysteries or science fiction, we need to combine the number of customers who purchased each type and subtract the number of customers who purchased both.
The number of customers who purchased mysteries is 34, and the number of customers who purchased science fiction is 27.
However, if we add these numbers together (34 + 27 = 61), we would be counting the customers who purchased both twice. So, we need to subtract the number of customers who purchased both from the total.
According to the survey, 13 customers purchased both mysteries and science fiction.
Therefore, the number of customers who purchased mysteries or science fiction is: 34 + 27 - 13 = 48.
Thus, 48 customers purchased mysteries or science fiction.
C) How many purchase exactly 2 types?
To find the number of customers who purchased exactly two types of novels, we need to add up the number of customers who purchased each combination of two types.
According to the survey, there were:
- 13 customers who purchased mysteries and science fiction.
- 10 customers who purchased mysteries and romance.
- 7 customers who purchased science fiction and romance.
- 3 customers who purchased all types.
Adding these numbers together: 13 + 10 + 7 + 3 = 33.
Therefore, 33 customers purchased exactly two types of novels.
I hope this explanation helped you understand the steps to solve the problem. If you have any further questions, feel free to ask!