To find \( P(\text{brown} | \text{black}) \), we use the formula for conditional probability:
\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]
In this case:
- Event A is choosing a brown pair of shoes.
- Event B is choosing a black pair of shoes.
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Finding \( P(B) = P(\text{black}) \): The probability of choosing a black pair of shoes is given by the number of black pairs divided by the total number of pairs:
\[ P(\text{black}) = \frac{47}{100} \]
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Finding \( P(A \cap B) = P(\text{brown} \cap \text{black}) \): This is the probability of randomly choosing a pair that is both brown and black. Since a pair cannot be both brown and black at the same time, this probability is 0:
\[ P(\text{brown} \cap \text{black}) = 0 \]
Now, substituting into the conditional probability formula:
\[ P(\text{brown} | \text{black}) = \frac{P(\text{brown} \cap \text{black})}{P(\text{black})} = \frac{0}{\frac{47}{100}} = 0 \]
Thus, \( P(brown | black) = 0 \).
Given the provided response options, none of them correctly represent \( P(brown | black) \). The correct answer is simply 0.