To determine the probability that a randomly selected person from the given survey does not take walks in the neighborhood but has a dog, we need to use the information provided in the two-way frequency table given:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline
\text{Dog Owner vs.} & 57 & \text{Does Not} & \text{Total} \\
\hline
\text{Walk Routine} & & \text{Walk} & \\
\text{Has a Dog} & & \text{} & \\
\hline
\text{Does Not Have} & 13 & 9 & 78 \\
\text{a Dog} & & & \\
\hline
\end{array}
\][/tex]
Here’s the step-by-step solution:
1. Identify the number of people who do not take walks but have a dog:
- According to the table, this group contains [tex]\(57\)[/tex] people.
2. Identify the total number of people surveyed:
- The table states that the total number of survey participants is [tex]\(78\)[/tex].
3. The probability of an event is the ratio of the number of favorable outcomes to the total number of possible outcomes:
[tex]\[
\text{Probability} = \frac{\text{Number of people with a dog who do not take walks}}{\text{Total number of people surveyed}}
\][/tex]
4. Substitute the given numbers into the probability formula:
[tex]\[
\text{Probability} = \frac{57}{78}
\][/tex]
Therefore, the probability that a randomly selected person from the survey does not take walks in the neighborhood but has a dog is:
[tex]\[
\frac{57}{78}
\][/tex]
