Geometry

Question Analysis
This question involves using Venn Diagrams and the concept of the complement of a compound event.
The main focus is on first finding the number of houses that have either a dog or a cat and then using that to determine the number of houses with neither, in order to calculate the probability.

Key Concept Explanation
We use the formula for the union of two sets, , to find the number of houses with either a dog or a cat. Then, the number of houses with neither is the total number of houses minus the number of houses with either. The probability of an event is the number of favorable outcomes divided by the total number of outcomes.

Step - by - Step Solution
Calculate the number of houses that have either a dog or a cat.
Using the formula , where (houses with a dog), (houses with a cat), and