1. **State the problem:** We need to find the probability of randomly choosing a blue or a yellow sock. 2. **Recall the formula for the union of two events:** $$P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$$ Since choosing a sock cannot be both blue and yellow at the same time, these events are mutually exclusive, so: $$P(\text{blue or yellow}) = P(\text{blue}) + P(\text{yellow})$$ 3. **Substitute the given probabilities:** $$P(\text{blue}) = \frac{1}{12}, \quad P(\text{yellow}) = \frac{3}{8}$$ 4. **Add the fractions:** Find a common denominator for $12$ and $8$, which is $24$. Convert each fraction: $$\frac{1}{12} = \frac{2}{24}, \quad \frac{3}{8} = \frac{9}{24}$$ 5. **Sum the fractions:** $$P(\text{blue or yellow}) = \frac{2}{24} + \frac{9}{24} = \frac{11}{24}$$ 6. **Final answer:** $$\boxed{\frac{11}{24}}$$ This fraction cannot be simplified further.