1. **State the problem:** We are given the probabilities of a student having ginger hair and blonde hair, and we need to find the probability that a student has either ginger or blonde hair. 2. **Given probabilities:** - Probability of ginger hair: $\frac{5}{14}$ - Probability of blonde hair: $\frac{9}{28}$ 3. **Formula used:** Since these two events are mutually exclusive (a student cannot have both ginger and blonde hair at the same time), the probability of either event occurring is the sum of their probabilities: $$P(\text{ginger or blonde}) = P(\text{ginger}) + P(\text{blonde})$$ 4. **Calculate the sum:** $$P = \frac{5}{14} + \frac{9}{28}$$ 5. **Find common denominator:** The least common denominator of 14 and 28 is 28. Convert $\frac{5}{14}$ to have denominator 28: $$\frac{5}{14} = \frac{5 \times 2}{14 \times 2} = \frac{10}{28}$$ 6. **Add the fractions:** $$P = \frac{10}{28} + \frac{9}{28} = \frac{10 + 9}{28} = \frac{19}{28}$$ 7. **Final answer:** The probability that a student chosen at random has either ginger or blonde hair is $$\boxed{\frac{19}{28}}$$