Question

the results of a survey of customers at a pet supply store showed that 35 owned geese, 31 owned mice, and 18 owned both geese and mice. how many owned either a goose or a mouse? of the customers surveyed, owned either a goose or a mouse. (type an integer or a decimal.)

Explanation:

Step1: Use the inclusion - exclusion principle

The formula for $|A\cup B|$ is $|A|+|B|-|A\cap B|$, where $A$ is the set of goose - owners and $B$ is the set of mouse - owners.
Let $|A| = 35$ (number of goose - owners), $|B|=31$ (number of mouse - owners) and $|A\cap B| = 18$ (number of owners of both).

Step2: Calculate the number of customers who owned either a goose or a mouse

$|A\cup B|=35 + 31-18$.
First, add 35 and 31: $35+31 = 66$.
Then subtract 18 from 66: $66-18=48$.

Answer:

48