Mr. Jay has 100 pairs of shoes in his closet. He has 26 brown pairs, 12 navy pairs, 47 black pairs, and 15 white pairs. What is P(brown|black) ?

Answer 1

To calculate the conditional probability \( P(\text{brown} | \text{black}) \), we need to understand what this probability represents. It is the probability of selecting a brown pair of shoes given that we have selected a black pair of shoes.

However, since brown and black pairs are mutually exclusive (you cannot have a shoe that is both brown and black), the probability of selecting a brown pair given that you have a black pair is \( 0 \).

Therefore, we can conclude:

\[ P(\text{brown} | \text{black}) = 0 \]