To solve this problem, we need to determine the percentage of students who passed the second exam and also passed the first exam, given the provided percentages.
Here's the step-by-step solution:
1. Identify the given percentages:
- The percentage of students who passed the second exam is [tex]\(60\%\)[/tex].
- The percentage of students who passed both exams is [tex]\(48\%\)[/tex].
2. Understand the relationship between the percentages:
- We are asked to find the percentage of students who passed the second exam that also passed the first exam.
3. Set up the problem:
- Let [tex]\(P(\text{Second})\)[/tex] represent the percentage of students who passed the second exam.
- Let [tex]\(P(\text{Both})\)[/tex] represent the percentage of students who passed both exams.
- We need to find [tex]\(P(\text{First} \mid \text{Second})\)[/tex], which is the conditional probability that a student passed the first exam given that they passed the second exam.
4. Use the conditional probability formula:
[tex]\[
P(\text{First} \mid \text{Second}) = \frac{P(\text{Both})}{P(\text{Second})} \times 100\%
\][/tex]
5. Substitute the given values into the formula:
[tex]\[
P(\text{First} \mid \text{Second}) = \frac{48\%}{60\%} \times 100\%
\][/tex]
6. Calculate the result:
[tex]\[
P(\text{First} \mid \text{Second}) = \frac{48}{60} \times 100\% = 0.8 \times 100\% = 80\%
\][/tex]
Therefore, [tex]\(80\%\)[/tex] of the students who passed the second exam also passed the first exam.
The correct answer is [tex]\( \boxed{80\%} \)[/tex].
