To find \( P(\text{brown} | \text{black}) \), we need to apply the formula for conditional probability:
\[ P(\text{brown} | \text{black}) = \frac{P(\text{brown and black})}{P(\text{black})} \]
In this case, since the categories of shoes are mutually exclusive (a pair of shoes cannot be both brown and black at the same time), \( P(\text{brown and black}) = 0 \). Thus, the only relevant factor we need to consider is how to evaluate the possibilities correctly.
Since we want to find the probability of selecting a brown pair given that we have selected a black pair, we can simplify our consideration:
- The total number of pairs of shoes is 100.
- There are 26 brown pairs.
- There are 47 black pairs.
However, since there are no brown and black pairs at once, the conditional probability in this context simplifies to simply considering the probability of each color, which doesn't directly exist.
The only reasonable approach here is to note that given we have a black pair, the probability of also having a brown pair remains unqualified as they are distinct.
Thus, the correct evaluation of the options is not listed since they don't represent \( P(\text{brown} | \text{black}) \) sufficiently.
Given the context and specified responses, the best foundational response would be:
\[ \text{None of the options directly give } P(\text{brown} | \text{black}) \]
But if you're looking at independence, since there is no overlap:
It simplifies further as \( \text{none} \) of those pairs can overlap and thus always return null probability in context.