In a recent survey of 100 women, the following information was gathered.
30 use shampoo A.
43 use shampoo B.
33 use shampoo C.
13 use shampoos A and B.
7 use shampoos A and C.
5 use shampoos B and C.
3 use all three.
How many are using shampoo A only (Region I)?
make a Venn diagram of 3 intersecting circles called A, B , and C
Put 3 in the intersection of all 3
Now look at the intersection of A and B, which is given as 13
But 3 have already been entered, so put 10 in the remaining part of A intersect B
in the same way the remaining part of A intersect C would be 4 and
the remaining part of B intersect C would be 2
now look at circle A, we have already entered 17, but there are 30 using A
So 13 would be using only A
Only B would be 28 and only C would be 24
Adding all those up only gives us 84
So unless I made some silly arithmetic error, it looks like 16 of the women don't use any of the three shampoos.
To find the number of women using shampoo A only (Region I), we need to subtract the number of women using shampoo A in combination with other shampoos from the total number of women using shampoo A.
From the given information:
- 30 women use shampoo A in total (including those who use it in combination with other shampoos).
- 13 women use shampoos A and B.
- 7 women use shampoos A and C.
- 3 women use all three shampoos (A, B, and C).
To find the number of women using shampoo A only, we need to subtract the number of women using shampoos A and B, the number of women using shampoos A and C, and the number of women using all three shampoos from the total number of women using shampoo A.
Therefore, the number of women using shampoo A only (Region I) can be calculated as:
30 - (13 + 7 + 3) = 30 - 23 = 7
Thus, 7 women are using shampoo A only (Region I).