A survey of 63 customers was taken at a bookstore regarding the types of books purchased. The survey found that 39 customers purchased mysteries, 29 purchased science fiction, 23 purchased romance novels, 16 purchased mysteries and science fiction, 13 purchased mysteries and romance novels, 9 purchased science fiction and romance novels, and 5 purchased all three types of books.
How many customers purchased only Science Fiction?
How many customers purchased only Romance?
How many customers purchased only Mysteries?
How many customers purchased both Science Fiction and Romance?
How many customers purchased both Science Fiction and Mysteries?
How many customers purchased both Romance and Mysteries?
How many customers purchased all three types?
To find the number of customers who purchased only Science Fiction, we need to subtract the number of customers who purchased both Science Fiction and Romance, and the number of customers who purchased all three types of books from the total number of customers who purchased Science Fiction.
The number of customers who purchased Science Fiction only = Total customers who purchased Science Fiction - Number of customers who purchased both Science Fiction and Romance - Number of customers who purchased all three types of books
Number of customers who purchased Science Fiction only = 29 - 9 - 5 = 15
Similarly, we can calculate the number of customers who purchased only Romance and only Mysteries.
The number of customers who purchased only Romance = Total customers who purchased Romance - Number of customers who purchased both Science Fiction and Romance - Number of customers who purchased all three types of books
Number of customers who purchased only Romance = 23 - 9 - 5 = 9
The number of customers who purchased only Mysteries = Total customers who purchased Mysteries - Number of customers who purchased both Mysteries and Romance - Number of customers who purchased all three types of books
Number of customers who purchased only Mysteries = 39 - 13 - 5 = 21
To find the number of customers who purchased both Science Fiction and Romance, we subtract the number of customers who purchased all three types of books from the number of customers who purchased both Science Fiction and Romance.
The number of customers who purchased both Science Fiction and Romance = Number of customers who purchased both Science Fiction and Romance - Number of customers who purchased all three types of books
Number of customers who purchased both Science Fiction and Romance = 9 - 5 = 4
Similarly, we can calculate the number of customers who purchased both Science Fiction and Mysteries, and both Romance and Mysteries.
The number of customers who purchased both Science Fiction and Mysteries = Number of customers who purchased both Science Fiction and Mysteries - Number of customers who purchased all three types of books
Number of customers who purchased both Science Fiction and Mysteries = 16 - 5 = 11
The number of customers who purchased both Romance and Mysteries = Number of customers who purchased both Mysteries and Romance - Number of customers who purchased all three types of books
Number of customers who purchased both Romance and Mysteries = 13 - 5 = 8
Finally, the number of customers who purchased all three types of books is given as 5.
To find the answers to these questions, we can use a method called the principle of inclusion-exclusion.
Let's break down the information given step by step:
1. The total number of customers surveyed is 63.
2. Let's start by finding the number of customers who purchased only Science Fiction. To do this, we need to subtract the customers who purchased both Science Fiction and other genres from the total number of Science Fiction buyers.
Number of customers who purchased both Science Fiction and Mysteries = 16
Number of customers who purchased both Science Fiction and Romance = 9
Number of customers who purchased all three types = 5
To find the number of customers who purchased only Science Fiction, we need to subtract these numbers from the total number of Science Fiction buyers.
Number of customers who purchased only Science Fiction = Total Science Fiction buyers - (Both Science Fiction and Mysteries + Both Science Fiction and Romance - All three types)
Number of customers who purchased only Science Fiction = 29 - (16 + 9 - 5)
Number of customers who purchased only Science Fiction = 29 - 20
Number of customers who purchased only Science Fiction = 9
Therefore, 9 customers purchased only Science Fiction.
3. Similarly, let's find the number of customers who purchased only Romance.
Number of customers who purchased both Romance and Mysteries = 13
Number of customers who purchased both Romance and Science Fiction = 9
Number of customers who purchased all three types = 5
To find the number of customers who purchased only Romance, we need to subtract these numbers from the total number of Romance buyers.
Number of customers who purchased only Romance = Total Romance buyers - (Both Romance and Mysteries + Both Romance and Science Fiction - All three types)
Number of customers who purchased only Romance = 23 - (13 + 9 - 5)
Number of customers who purchased only Romance = 23 - 17
Number of customers who purchased only Romance = 6
Therefore, 6 customers purchased only Romance.
4. Now, let's find the number of customers who purchased only Mysteries.
Number of customers who purchased both Mysteries and Science Fiction = 16
Number of customers who purchased both Mysteries and Romance = 13
Number of customers who purchased all three types = 5
To find the number of customers who purchased only Mysteries, we need to subtract these numbers from the total number of Mysteries buyers.
Number of customers who purchased only Mysteries = Total Mysteries buyers - (Both Mysteries and Science Fiction + Both Mysteries and Romance - All three types)
Number of customers who purchased only Mysteries = 39 - (16 + 13 - 5)
Number of customers who purchased only Mysteries = 39 - 24
Number of customers who purchased only Mysteries = 15
Therefore, 15 customers purchased only Mysteries.
5. Next, let's find the number of customers who purchased both Science Fiction and Romance.
Number of customers who purchased both Science Fiction and Romance = 9
Therefore, 9 customers purchased both Science Fiction and Romance.
6. Similarly, let's find the number of customers who purchased both Science Fiction and Mysteries.
Number of customers who purchased both Science Fiction and Mysteries = 16
Therefore, 16 customers purchased both Science Fiction and Mysteries.
7. Now, let's find the number of customers who purchased both Romance and Mysteries.
Number of customers who purchased both Romance and Mysteries = 13
Therefore, 13 customers purchased both Romance and Mysteries.
8. Finally, let's find the number of customers who purchased all three types.
Number of customers who purchased all three types = 5
Therefore, 5 customers purchased all three types.
To summarize the answers to the questions:
- Number of customers who purchased only Science Fiction = 9
- Number of customers who purchased only Romance = 6
- Number of customers who purchased only Mysteries = 15
- Number of customers who purchased both Science Fiction and Romance = 9
- Number of customers who purchased both Science Fiction and Mysteries = 16
- Number of customers who purchased both Romance and Mysteries = 13
- Number of customers who purchased all three types = 5
Make a Venn diagram. All the data can be nicely entered.
Once done, all your answers can be determined from that.