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The question asks to determine whether events \( A \) and \( B \) are mutually exclusive.

### Given Events:
- **Event A**: At least 4 of the students are majoring in psychology.
- **Event B**: Fewer than 4 of the students are majoring in psychology.

### Explanation:
- **Mutually exclusive events** are events that **cannot happen at the same time**. In other words, if one event occurs, the other cannot occur.

Here:
- Event \( A \) involves having **at least 4 students majoring in psychology**.
- Event \( B \) involves having **fewer than 4 students majoring in psychology**.

Clearly, these two events **cannot both occur simultaneously** because either there are at least 4 students majoring in psychology, or there are fewer than 4, but not both at the same time.

### Conclusion:
The events \( A \) and \( B \) are **mutually exclusive**.

Would you like more details on this? Let me know if you have any questions.

Here are some related questions to think about:
1. What are some examples of non-mutually exclusive events?
2. How do mutually exclusive events affect probability calculations?
3. What is the formula for calculating the probability of mutually exclusive events?
4. Can two mutually exclusive events have non-zero probabilities?
5. How does the concept of mutually exclusive events differ from independent events?

**Tip:** When solving probability problems, always check if the events are mutually exclusive or independent. This distinction impacts the formulas and approach you'll use!

Determine whether events A and B are mutually exclusive.
A sample of 25 students is selected from the list of all students in a large statistics class.
A: At least 4 of the students are majoring in psychology.
B: Fewer than 4 of the students are majoring in psychology.

Learn how to determine whether events A and B are mutually exclusive. Event A involves at least 4 students majoring in psychology, while Event B involves fewer than 4. Understand the concept of mutually exclusive events in probability and why these two events cannot happen at the same time. Suitable for students in Grades 10-12.

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