A survey of 60 customers was taken at a
bookstore regarding the types of books purchased. The survey found that
36 customers purchased mysteries
28 purchased science fiction
19purchased romance novels
14 purchased mysteries and science fiction
10 purchased mysteries and romance novels
7 purchased science fiction and romance novels
3 purchased all three types of books.
So, how many purchased mysteries but not romance novels?
There are different methods to approach this problem, but one way is to use a Venn diagram. First, we can draw three intersecting circles to represent the three types of books:
M
/ \
MSR SRF
where M represents mysteries, S represents science fiction, and R represents romance novels. The overlapping parts represent the customers who purchased more than one type of book, and the area where all three circles intersect represents the customers who purchased all three types.
Next, we can fill in the numbers from the survey:
36
/ \
10 14
/ \
3 7
/ \
19
For example, 36 customers purchased mysteries, so we write "36" in the M circle. 14 customers purchased both mysteries and science fiction, so we write "14" in the overlap between M and S. And so on.
Now we can use the Venn diagram to find the answer. We want to know how many customers purchased mysteries but not romance novels. This corresponds to the part of the M circle that is outside the R circle:
36
/ \
10 14
/ \
3 7
/ \
19
To find this number, we need to subtract the customers who purchased both mysteries and romance novels (the overlap between M and R) from the total number of customers who purchased mysteries (the whole M circle):
36 - 10 - 3 = 23
Therefore, 23 customers purchased mysteries but not romance novels.
The probability that an African American person in the US has type O+ blood is 47%.
Four unrelated African Americans]are selected at random. Find the probability that all of the four have type O+ blood.
Since the four African Americans are selected at random, we can assume that their blood types are independent. That is, the probability of each person having type O+ blood is the same and does not depend on the others.
The probability that one African American person has type O+ blood is 47%, so the probability that all four of them have type O+ blood is:
0.47 x 0.47 x 0.47 x 0.47 = 0.047^4 = 0.00002622
Therefore, the probability that all four unrelated African Americans selected at random have type O+ blood is approximately 0.00002622.
To find out how many customers purchased mysteries but not romance novels, we need to subtract the number of customers who purchased both mysteries and romance novels from the total number of customers who purchased mysteries.
According to the given information:
- 36 customers purchased mysteries in total.
- 10 customers purchased mysteries and romance novels.
Therefore, the number of customers who purchased mysteries but not romance novels can be calculated as:
36 - 10 = 26
So, 26 customers purchased mysteries but not romance novels.