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The problem asks for the probability of a student meeting graduation criteria for both a Bachelor of Arts and Science degree.

We are provided with the following information:
- \( P(\text{Science}) = 0.3 \)
- \( P(\text{Arts}) = 0.6 \)
- \( P(\text{no degree}) = 0.2 \)
- \( P(\text{Arts} | \text{Science}) = 0.24 \), which is the probability of getting an Arts degree given that the student is already getting a Science degree.

The key here is that we are trying to find the probability of getting both degrees. This is calculated as:
\[
P(\text{Arts and Science}) = P(\text{Science}) \times P(\text{Arts} | \text{Science})
\]

Substitute the given values:
\[
P(\text{Arts and Science}) = 0.3 \times 0.24 = 0.072
\]

Thus, the probability of a student meeting the criteria for both degrees is **0.072**.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. How do you calculate conditional probability?
2. What does \( P(\text{Arts} | \text{Science}) \) represent in terms of dependent events?
3. How would you compute the probability if \( P(\text{Science}) \) were different?
4. Can a student meet both graduation criteria without completing either degree? Why or why not?
5. How would the calculation change if the probability of not getting any degree (\( P(\text{no degree}) \)) were relevant here?

**Tip:** Conditional probability is useful in scenarios where the outcome of one event affects the probability of another.

What is the probability of a student meeting graduation criteria for both a Bachelor of Arts and Science degree?

This problem explores the probability of a student meeting graduation criteria for both a Bachelor of Arts and Science degree. It involves key concepts in conditional probability and dependent events, using the formula P(Arts and Science) = P(Science) * P(Arts | Science).

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