To find \( P(\text{brown} | \text{black}) \), which is the probability of selecting a brown pair of shoes given that a black pair has been selected, we can use the formula for conditional probability. The formula is:
\[ P(A | B) = \frac{P(A \cap B)}{P(B)} \]
Where:
- \( A \) is the event of selecting a brown pair.
- \( B \) is the event of selecting a black pair.
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Identify \( P(B) \), the total probability of selecting a black pair:
- There are 47 black pairs of shoes out of 100 pairs in total.
- Thus, \( P(B) = \frac{47}{100} \).
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Identify \( P(A \cap B) \), the probability of selecting a pair that is both brown and black. Since pairs cannot be both brown and black at the same time (they are distinct categories), this implies that:
- \( P(A \cap B) = 0 \).
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Calculate \( P(A | B) \): \[ P(\text{brown} | \text{black}) = \frac{P(\text{brown} \cap \text{black})}{P(\text{black})} = \frac{0}{\frac{47}{100}} = 0 \]
Since it is not possible to have a pair of shoes that is both brown and black, the probability \( P(\text{brown} | \text{black}) \) is \( 0 \).
The answer choice that corresponds to a zero probability isn't provided, but logically, it is \( 0 \).