Question

A state university offers need-based partial scholarships to 25% of accepted first-year students who apply for the scholarship program. Work-study positions are far more common, with 55% of first-year students getting a work-study arrangement. What are the chances of a first-year student earning either a partial-ride scholarship or a work-study job? (1 point) Responses 50% 50% 56% 56% 66% 66% 80%

Answer 1

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%**.