Alright, let's break this down step-by-step to find the probability that a randomly chosen person from this group owns a dog.
1. Number of people who responded "yes":
We know that 130 people responded that they own a dog.
2. Number of people who responded "no":
We know that 428 people responded that they do not own a dog.
3. Calculate the total number of responses:
To find the total number of people who were surveyed, we add the number of "yes" responses and "no" responses:
[tex]\[
\text{Total responses} = \text{Number of "yes" responses} + \text{Number of "no" responses} = 130 + 428 = 558
\][/tex]
4. Determine the probability that a randomly chosen person owns a dog:
Probability is calculated as the number of favorable outcomes divided by the total number of possible outcomes. In this case, the favorable outcome is someone who owns a dog ("yes" response):
[tex]\[
\text{Probability} = \frac{\text{Number of "yes" responses}}{\text{Total responses}} = \frac{130}{558}
\][/tex]
So, the probability that a randomly chosen person owns a dog is:
[tex]\[
\frac{130}{558}
\][/tex]
Among the provided options:
- [tex]\(\frac{130}{428}\)[/tex] is incorrect because 428 represents the number of "no" responses, not the total.
- [tex]\(\frac{298}{130}\)[/tex] is incorrect because 298 is not relevant to our calculation.
Therefore, the correct option is:
[tex]\[
\frac{130}{558}
\][/tex]
Numerically, this probability is approximately [tex]\(0.233\)[/tex], indicating that there is roughly a 23.3% chance that a randomly selected person from this group owns a dog.
