In a recent survey of 100 women, the following information was gathered.
31 use shampoo A.
27 use shampoo B.
36 use shampoo C.
8 use shampoos A and B.
3 use shampoos A and C.
5 use shampoos B and C.
1 use all three.
Use the figure to answer the question in the problem.
How many are using shampoos A and C, but not B (Region IV)?
1 . women
I don't know how to get this answer help me please
Make a Venn diagram. Label the small center section with 1, since only 1 person uses all 3.
Now label the intersection of A&B with 8, and the intersection of A&C with 3.
Now the portion of A outside B and C is 31-8-3-1 = 19.
Moving right along, you will see that the answer is 3
To determine how many women are using shampoos A and C, but not B (Region IV), we need to analyze the given information.
From the survey, we know that:
- 31 women use shampoo A
- 27 women use shampoo B
- 36 women use shampoo C
- 8 women use both shampoos A and B
- 3 women use both shampoos A and C
- 5 women use both shampoos B and C
- 1 woman uses all three shampoos (A, B, and C)
We can use a Venn diagram to visualize this information, with circles representing shampoo A, shampoo B, and shampoo C, and the overlapping regions indicating the number of women using multiple shampoos.
To find the number of women using shampoos A and C but not B (Region IV), we need to subtract the number of women using A, B, and C (the intersection of all three shampoos) from the number of women using A and C (the intersection of shampoos A and C). In other words, we need to find the value in Region IV.
From the given information, we know that 3 women use both shampoos A and C. However, since we are looking for women using shampoos A and C but not B, we need to exclude the women using all three shampoos (1 woman). Therefore, we have:
Number of women using shampoos A and C, but not B = Women using shampoos A and C - Women using all three shampoos
= 3 - 1
= 2
Therefore, there are 2 women using shampoos A and C, but not B (Region IV).