Problem Solving

Please help me solve this:

Of the 100 pet owners who respond to a survey, 50 own cats, 42 own dogs, and 7 own both. How many respondents own neither a cat nor a dog?

a. 7
b. 8
c. 10
d. 12
e. 15

jcnissi wrote:Please help me solve this:

Of the 100 pet owners who respond to a survey, 50 own cats, 42 own dogs, and 7 own both. How many respondents own neither a cat nor a dog?

a. 7
b. 8
c. 10
d. 12
e. 15

P (AUB) = P(A) + p(B) - P(AnB)
= 50 +42 -7
=85
Total = p(AUB) + Neither of( A or B)

100 = 85 + Neither of( A or B)

Neither of( A or B)
= 15

Pick[spoiler] E[spoiler[/spoiler]][/spoiler]

jcnissi wrote:Please help me solve this:

Of the 100 pet owners who respond to a survey, 50 own cats, 42 own dogs, and 7 own both. How many respondents own neither a cat nor a dog?

a. 7
b. 8
c. 10
d. 12
e. 15

In words rather than symbols:

True # of items = (total # in group 1) + (total # in group 2) + (# in neither) - (# in both groups)

or, more simply:

True # = G1 + G2 + neither - both

In this question:

True # = 100
Cats = 50
Dogs = 42
Both = 7

So:

100 = 50 + 42 + neither - 7

100 = 85 + neither

15 = neither... choose (E).

total=100
c=50
d=42
c and d=7

only c=50-7=43
only d=35

total people who own animals= 43+35+7=85
people who do not own animals=100-85=15
E

jcnissi wrote:Please help me solve this:

Of the 100 pet owners who respond to a survey, 50 own cats, 42 own dogs, and 7 own both. How many respondents own neither a cat nor a dog?

a. 7
b. 8
c. 10
d. 12
e. 15