A math teacher gave a class two exams. There was 30% of the class who passed both exams and 58% of the class passed the first exam.

What percent of those who passed the first exam also passed the second exam?

Round your answer to three decimal places.

Let's solve this problem step by step.

We know the following:
- 30% of the class passed both exams.
- 58% of the class passed the first exam.

We are asked to find what percent of those who passed the first exam also passed the second exam. This is equivalent to finding the conditional probability \( P(\text{Passed second} | \text{Passed first}) \).

The conditional probability formula is:

\[
P(\text{Passed second} | \text{Passed first}) = \frac{P(\text{Passed both})}{P(\text{Passed first})}
\]

### Substituting the known values:
- \( P(\text{Passed both}) = 30\% = 0.30 \)
- \( P(\text{Passed first}) = 58\% = 0.58 \)

\[
P(\text{Passed second} | \text{Passed first}) = \frac{0.30}{0.58} \approx 0.517
\]

### Conclusion:
The percentage of those who passed the first exam and also passed the second exam is approximately \( 51.7\% \).

Would you like further details or have any questions?

Here are five related questions:
1. How would you calculate the probability of passing only the second exam?
2. What if 65% of the class passed the second exam, how would that affect the calculations?
3. Can we calculate the total percentage of students who passed at least one exam?
4. What if 10% of the class failed both exams, how would that change the analysis?
5. How could a Venn diagram be used to visualize this problem?

**Tip:** Conditional probability helps you focus on a specific subset of the total population to make more accurate predictions.

A math teacher gave a class two exams. There was 30% of the class who passed both exams and 58% of the class passed the first exam. What percent of those who passed the first exam also passed the second exam? Round your answer to three decimal places.

Calculate the conditional probability of passing the second exam given that 30% passed both exams and 58% passed the first exam. This detailed explanation walks through the steps using the conditional probability formula. Suitable for students in Grades 9-12.

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