If the probability of Tiffany pulling out a white pair of shoes is \( \frac{2}{5} \), then the probability of her pulling out a black pair of shoes can be calculated using the fact that the total probability must equal 1.
Let \( P(\text{black}) \) be the probability of pulling out a black pair of shoes.
So:
\[ P(\text{white}) + P(\text{black}) = 1 \]
Substituting the known probability of white shoes:
\[ \frac{2}{5} + P(\text{black}) = 1 \]
To find \( P(\text{black}) \), we can rearrange the equation:
\[ P(\text{black}) = 1 - \frac{2}{5} \]
Converting 1 into a fraction with the same denominator, we have:
\[ 1 = \frac{5}{5} \]
Now, substitute:
\[ P(\text{black}) = \frac{5}{5} - \frac{2}{5} = \frac{3}{5} \]
Therefore, the chance of Tiffany randomly pulling out a black pair of shoes is \( \frac{3}{5} \).