To find the conditional probability \( P(A|B) \), where event \( A \) is selecting a brown animal and event \( B \) is selecting a cat, we use the formula:
\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]
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Identify \( P(A \cap B) \):
- This is the probability of selecting a brown cat. From the table, the number of brown cats is 9.
- Total animals in the shelter is 72.
- Therefore, \( P(A \cap B) = \frac{9}{72} \).
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Identify \( P(B) \):
- This is the probability of selecting a cat. The total number of cats is 38.
- Therefore, \( P(B) = \frac{38}{72} \).
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Calculate \( P(A|B) \):
- Now plug the values into the conditional probability formula:
\[ P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{\frac{9}{72}}{\frac{38}{72}} \]
This simplifies to:
\[ P(A|B) = \frac{9}{38} \]
- Convert to percentage:
- To express this as a percentage, we multiply by 100:
\[ P(A|B) = \frac{9}{38} \times 100 \approx 23.68% \]
- Round to the nearest whole number:
- Rounding 23.68% gives us approximately 24%.
So, the final answer is:
\[ P(A|B) \text{ is } \textbf{24} \text{ %}. \]