please help with this petsmart statistical probability question!!

Question

Customers entering Petsmart were surveyed at random about what type of pet they had. The results showed that the probabitlity of a person owning a dog was .56. The probabilty that a person had both a dog and a cat was .20 and the probability that the customer had neither a dog nor a cat was .12.

What is the probability that a customer has only cats?

Answer 1

Use whole numbers for percents

T = 100 (total)

D = x + z = 56 (dog)

D&C = z = 20

w = 12

T = w + x + y + z

T = 12 + 56 + y = 100

68 + y = 100

y = 32

probability that a customer has only cats = 0.32

Answer 2

Drawing a Venn diagram will be helpful.

Prob(dog) includes Prob(dog only) and Prob(dog + cat)

P(Dog only) = 0.56 - P(both dog and cat) = 0.56 - 0.2 = 0.36

P(neither) = 0.12. given to us in problem

Sum of all probabilities should be 1.

P(Dog only) + P(both) + P(Cat only) + P(neither) = 1

0.36 + 0.2 + P(Cat only) + 0.12 = 1

Hence P(Cat only) = 1 - 0.36 - 0.2 - 0.12 = 0.32