To find \( P(\text{brown} | \text{black}) \), which represents the probability of having a brown pair of shoes given that a black pair has been chosen, we can use the formula for conditional probability:
\[ P(A | B) = \frac{P(A \cap B)}{P(B)} \]
In this case, \( A \) is the event of choosing a brown pair of shoes, and \( B \) is the event of choosing a black pair of shoes.
However, since choosing a black pair of shoes does not affect the total number of brown pairs, we can observe that knowing we have a black pair means we are left with 99 pairs of shoes overall (100 total - 1 black pair). The total number of brown pairs remains 26.
To compute \( P(brown) \) and \( P(black) \):
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\( P(\text{black}) \): The probability of selecting a black pair initially. There are 47 black pairs out of 100. \[ P(\text{black}) = \frac{47}{100} \]
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\( P(\text{brown and black}) \): Since brown and black are independent events (choosing one doesn't change the number of the other), the probability of selecting one brown after a black has been chosen does not use the previously selected one. Therefore, after choosing black, the probability of next choosing brown is the number of brown pairs divided by the remaining pairs: \[ P(\text{brown | black}) = \frac{26}{99} \]
We can consolidate this information into one result:
- Probabilities are calculated when items are NOT mutually occurring (just from the context that choosing one doesn't directly impact the number of the other choice relevantly).
Hence, the possible answers provided do not correlate directly with the stated calculation as option B or similar doesn't hold relevance for both singular event occurrences.
Thus, among provided options: None of those options are correctly denoting the calculation or concept of \( P(brown | black) \) as per standard probability concept for this instance.
Correctly it would rather signal back to:
- \( 0 \) relevance towards brown if black was indeed choiced instead via chance conceptual calculations.
Please note, if these were included to vary the proposed calculations that could apply in a conceptual evaluative manner, they don't exactly fit the conditional space directs hence none actually matches \( P(brown | black) \) adequacy as defined.