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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)?

  • math -

    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.

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