Some researchers claim there is an association between owning a dog and developing a flea infestation at home. They took a random sample of people living in St. Louis, Missouri, and recorded whether they had a dog and whether they had a flea infestation in their home. The results are shown in the following two-way relative frequency table:

Has Flea Infestation	Does Not Have Flea Infestation	Row Totals
Does not have a dog	0.015	0.652	0.667
Has one dog	0.022	0.261	0.283
Has more than one dog	0.032	0.019	0.050
Column Totals	0.069	0.931	1

What is the conditional relative frequency of having more than one dog, given there is a flea infestation? Round your answer to the nearest thousandths place.
0.069
0.050
0.283
0.464

To find the conditional relative frequency of having more than one dog, given that there is a flea infestation, we need to use the formula for conditional probability:

\[
P(\text{More than one dog | Flea infestation}) = \frac{P(\text{More than one dog and Flea infestation})}{P(\text{Flea infestation})}
\]

From the table:

- \( P(\text{More than one dog and Flea infestation}) = 0.032 \)
- \( P(\text{Flea infestation}) = 0.069 \)

Now, calculate the conditional probability:

\[
P(\text{More than one dog | Flea infestation}) = \frac{0.032}{0.069}
\]

Let's compute this:

\[
P(\text{More than one dog | Flea infestation}) \approx 0.464
\]

Thus, the conditional relative frequency is **0.464**.

Would you like more details or have any questions about this? Here are some related questions to deepen your understanding:

1. What is conditional probability, and how is it used in statistical analysis?
2. How do relative frequencies differ from absolute frequencies?
3. What other insights can be derived from this two-way table?
4. How could a larger sample size impact the accuracy of these results?
5. What assumptions might researchers need to consider when interpreting these findings?

**Tip:** Conditional probability helps in understanding how two events are related when one event has already occurred.

What is the conditional relative frequency of having more than one dog, given there is a flea infestation? Round your answer to the nearest thousandths place.

Explore how to calculate the conditional probability of owning more than one dog given a flea infestation, using data from a two-way frequency table. This problem demonstrates key statistical concepts, such as conditional probability and relative frequency, suitable for students in Grades 9-12.

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