If the probability of Tiffany pulling out a white pair of shoes is \( \frac{2}{5} \), then the remaining probability for pulling out black shoes can be found by subtracting the probability of pulling out white shoes from 1.
The total probability must equal 1:
\[ \text{Probability of white shoes} + \text{Probability of black shoes} = 1 \]
Let \( P(B) \) be the probability of pulling out a black pair of shoes. Then:
\[ \frac{2}{5} + P(B) = 1 \]
To find \( P(B) \):
\[ P(B) = 1 - \frac{2}{5} = \frac{5}{5} - \frac{2}{5} = \frac{3}{5} \]
Thus, the probability of Tiffany randomly pulling out a black pair of shoes is \( \frac{3}{5} \).