A teacher gave her students two tests. If 45% of the students passed both tests and 60% passed the first test, what is the probability that a student who passed the first test also passed the second? Round your answer to the nearest percent.

Answer

To solve the problem, we need to find the probability that a student who passed the first test also passed the second test. We can use the information given in the question to find this probability.

### Step-by-step Solution:

1. **Identify the given information:**
- Let \( P(A) \) be the probability that a student passed the first test.
- Let \( P(B) \) be the probability that a student passed the second test.
- Let \( P(A \cap B) \) be the probability that a student passed both tests.
- From the problem, we know:
- \( P(A) = 0.60 \) (60% passed the first test)
- \( P(A \cap B) = 0.45 \) (45% passed both tests)

2. **Use the formula for conditional probability:**
The probability that a student who passed the first test also passed the second test is given by:
\[ P(B|A) = \frac{P(A \cap B)}{P(A)} \]
where \( P(B|A) \) is the probability of passing the second test given that the student passed the first test.

3. **Substitute the known values into the formula:**
\[ P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.45}{0.60} \]

4. **Calculate the probability:**
\[ P(B|A) = \frac{0.45}{0.60} = 0.75 \]

5. **Convert to percentage:**
To express this probability as a percentage, we multiply by 100:
\[ P(B|A) = 0.75 \times 100 = 75\% \]

6. **Round the answer:**
Since the answer is already a whole number, we can state that the probability that a student who passed the first test also passed the second test is:
\[ \text{Probability} = 75\% \]

### Final Answer:
The probability that a student who passed the first test also passed the second test is **75%**.