1. **State the problem:** A dog shelter has 6 German shepherds, 16 chihuahuas, 8 pit bulls, and 20 mix breeds. We want to find the probability that a randomly selected dog is either a chihuahua or a pit bull. 2. **Formula for probability:** The probability of an event is given by $$P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$$ 3. **Calculate total number of dogs:** $$6 + 16 + 8 + 20 = 50$$ 4. **Calculate number of favorable outcomes:** Dogs that are chihuahuas or pit bulls: $$16 + 8 = 24$$ 5. **Calculate the probability:** $$P = \frac{24}{50}$$ 6. **Simplify the fraction:** $$P = \frac{\cancel{24}^{12}}{\cancel{50}^{25}} = \frac{12}{25}$$ 7. **Final answer:** The probability that the dog selected is either a chihuahua or a pit bull is $$\boxed{\frac{12}{25}}$$