Question

In a certain community, 73% of the residents own a dog, 49% of the residents own a cat, and 35% of all cat owners own a dog.

(a) Find the proportion of residents that own both a dog and a cat.

Answer 1

To solve the mathematical problem completely, the proportion of residents that own both a dog and a cat is 17.15%, calculated by multiplying 35% of cat owners by 49% total cat-owning residents.

Step-by-step explanation:

To find the proportion of residents that own both a dog and a cat in a certain community, given the percentages of dog owners, cat owners, and the percentage of cat owners who also own dogs, we can use the concept of probability and overlapping sets.

We know 73% of residents own a dog and 49% own a cat. Importantly, we are told that 35% of all cat owners also own a dog.

First, let's find out the actual percentage of cat owners who also own a dog. Since 35% of cat owners own a dog and there are 49% of residents who own a cat, we multiply these two percentages to find the proportion of all residents that own both a dog and a cat:

Proportion of residents who own both a dog and a cat = 35% of 49% = 0.35 * 0.49 = 0.1715 or 17.15%.

Therefore, 17.15% of the community's residents own both a dog and a cat. This percentage represents the overlap between the two groups of pet owners in the community.