To find the conditional probability \( P(\text{brown} | \text{black}) \), we use the formula for conditional probability:
\[ P(A | B) = \frac{P(A \cap B)}{P(B)} \]
In this context:
- Let \( A \) be the event that a pair of shoes is brown.
- Let \( B \) be the event that a pair of shoes is black.
Since the events are mutually exclusive (a pair of shoes cannot be both brown and black), \( P(A \cap B) = 0 \).
However, if you're looking for the conditional probability in a different context where you choose a pair of shoes and want to know the probability of it being brown given that you have chosen a black pair beforehand, then the correct way to represent it would be:
- Total pairs of shoes = 100.
- Pairs of brown = 26.
- Pairs of black = 47.
Thus, since the choice of a black pair of shoes does not influence the total number of brown shoes, we just focus on \( P(\text{brown}) \):
Now, since there are no brown and black pairs simultaneously, the conditional probability \( P(\text{brown} | \text{black}) \) simplifies out to:
Since the pair could not be both brown and black, you would be looking at an abstract situation where picking one color doesn't affect the pool remaining:
The responses you have listed are not clearly applicable in this case of mutually exclusive events.
Thus the polished concept towards the conditional probability might yield that \( P(\text{brown | black}) \) remains contextual, situational probability perspectives on disjoint events would rather depict no effective relationship as \( P(brown) \) upon the condition of black shoes.
Hence the most reasonable answer from the choices you've listed does not apply directly, as conditional probability would yield zero if calculated literally through the events. You may need to specify an intended context for these chosen distributions.
If it's meant as the probability of choosing brown from non-black remaining pairs:
\[ = \frac{26}{100} \]
But it's implied distinctively the chances broaden into 0 resultant through black instantiation without elaborating.
In conclusion, if interpreted purest, this indicates no possibility of choosing resulting brown given a prior black chosen due to non-overlapping characteristics. The immediate option here needs reconciling with properly filtered understanding of those choices listed initially.