In a recent survey of 100 women, the following information was gathered.
36 use shampoo A.
37 use shampoo B.
38 use shampoo C.
14 use shampoos A and B.
8 use shampoos A and C.
9 use shampoos B and C.
3 use all three.
Use the figure to answer the question in the problem.
How many are using shampoo A only (Region I)?
The question is best answered with a Venn diagram.
Start with those that use all three.
14 use A & B, so 14-3=11 use A & B but not C.
8 use A & C, so 8-3=5 use A & C but not C.
So those who use A only
A only = 36-(11+3+5)=17
To determine the number of people who are using shampoo A only (Region I), we need to exclude those who are using shampoos B and C from the total number of people using shampoo A.
From the given information, we know that:
- 36 use shampoo A in total.
- 14 use shampoos A and B.
- 8 use shampoos A and C.
To find the number of people using shampoo A only, we will subtract the number of people using shampoos A and B, and those using shampoos A and C from the total number of people using shampoo A.
Number of people using shampoo A only = Total number of people using shampoo A - Number of people using shampoos A and B - Number of people using shampoos A and C
Number of people using shampoo A only = 36 - 14 - 8
Number of people using shampoo A only = 14
Therefore, there are 14 people using shampoo A only (Region I) based on the given information.