To find the probability of a first-year student earning either a partial-ride scholarship or a work-study job, we can use the principle of inclusion-exclusion.
Let's denote:
- \( P(S) \) = probability of getting a scholarship = 25% = 0.25
- \( P(W) \) = probability of getting a work-study job = 55% = 0.55
Assuming that getting a scholarship and getting a work-study job are independent events, the probability of a student getting neither can be calculated first:
\[ P(\text{not } S) = 1 - P(S) = 1 - 0.25 = 0.75 \] \[ P(\text{not } W) = 1 - P(W) = 1 - 0.55 = 0.45 \]
Now, the probability of not getting either a scholarship or a work-study job is:
\[ P(\text{not } S \text{ and not } W) = P(\text{not } S) \times P(\text{not } W) = 0.75 \times 0.45 = 0.3375 \]
Therefore, the probability of getting at least one (either a scholarship or a work-study job) is:
\[ P(S \text{ or } W) = 1 - P(\text{not } S \text{ and not } W) = 1 - 0.3375 = 0.6625 \]
Converted to a percentage, this is approximately 66.25%.
Thus, the closest response is 66%.