In a survey of 154 pet owners, 56 said they own a dog, and 76 said they own a cat. 11 said they own both a dog and a cat. How many owned neither a cat nor a dog?

Question

In a survey of 154 pet owners, 56 said they own a dog, and 76 said they own a cat. 11 said they own both a dog and a cat. How many owned neither a cat nor a dog?

Answer 1

It helps to draw a Venn diagram, two overlapping circles inside a rectangle

the overlap =11

56-11 = 45 solely in one circle

76-11 = 65 solely in the other circle

add them up 11+45+65 = 121

subtract 154-121 = 33 who own neither a cat or a dog

or use probability theory

P(~D&~C) = 1 -P(D) - P(C) -+P(D&C) = 1-56/154 - 76/154 -+/154

multiply by 154

154 -56-76+11

=154-141+11

=165-132

33 own neither