Given scenario is:
A pet store keeps track of the purchases of customers over a four-hour period. The store
manager classifies purchases as containing a dog product, a cat product, a fish product or
product for a different kind of pets. She found.
83 purchased a dog product
101 purchased a cat product
22 purchased a fish product
31 purchased a dog and a cat product
08 purchased a dog and fish product
10 purchased a cat and fish product
06 purchased a dog, cat and a fish product
34 purchased a product for a pet other than a dog, cat or fish
a) How many purchases were for a dog product only?
b) How many purchases were for a cat product only?
c) How many purchases were for a dog or fish product?
d) How many purchases were there in total?
Answers
SOLUTION
GIVEN
A pet store keeps track of the purchases of customers over a four-hour period. The store manager classifies purchases as containing a dog product, a cat product, a fish product or product for a different kind of pets
TO DETERMINE
a) How many purchases were for a dog product only?
b) How many purchases were for a cat product only?
c) How many purchases were for a dog or fish product?
d) How many purchases were there in total?
EVALUATION
Let C , D , F denotes the set of purchases for cat , dog and fish product respectively
Now it is given that
83 purchased a dog product
101 purchased a cat product
22 purchased a fish product
31 purchased a dog and a cat product
8 purchased a dog and fish product
10 purchased a cat and fish product
6 purchased a dog, cat and a fish product
34 purchased a product for a pet other than a dog, cat or fish
We draw the venn diagram
Venn Diagram : Venn Diagram is referred to the attachment
(a) The number of purchases for a dog product only
= n( Purchases for a dog product only )
= 83 - 25 - 6 - 2
= 50
(b) The number of purchases for a cat product only
= n( Purchases for a cat product only )
= 101 - 25 - 6 - 4
= 66
(c) The number of purchases were for a dog or fish product
= n( D ∪ F )
= 50 + 25 + 6 + 4 + 2 + 10
= 97
(d) The total number of purchases for a dog, cat or fish product
= n( C ∪ D ∪ F )
= 50 + 25 + 66 + 2 + 6 + 4 + 10
= 163
Now 34 purchased a product for a pet other than a dog, cat or fish
So the total number of purchases
= 163 + 34
= 197
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