tal) In a survey of 185 college students, they were asked whether they have dogs, cats,

or birds as pets:

90 have dogs,

68 have cats,

8 have birds only,

15 have both cats and dogs only,

20 have both birds and dogs,

12 have both cats and birds, and

7 students have all three animals as pets

a). Draw a Venn diagram to represent the given information.

b). How many students have cats only?

c). What proportion of the students have exactly one type of animal as pets?

a) We have drawn three circles, labeled D, C, B representing students who have dogs, cats, and birds, respectively. Based on the given information we can fill numbers in for all three animals (7), cats and dogs only (15), and birds only (8).

Then we can fill in cats and birds only by subtracting the number with all three. That will be 12 -7 = 5. Birds and dogs only is similarly filled by subtracting all three to get 20 -7 = 13 birds and dogs only.

Dogs only is found by subtracting the numbers in multiple categories from the total number of dogs: 90 -13 -7 -15 = 55. Cats only is found the same way: 68 -5 -7 -15 = 41.

The completed diagram is shown in the attachment. (We haven't figured the quantity for "none.")

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b) 41 students have cats only

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c) The total number with dogs only, cats only, or birds only is ...

55 +41 +8 = 104

Of the 185 total students, that is 104/185 ≈ 56.2%.

56.2% of students have exactly one type of animal as a pet.