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.