Two mutually exclusive events having nonzero probabilities of occurrence cannot be ________?

Answer

To solve the question, we need to understand the concepts of mutually exclusive events and independent events in probability.

### Step-by-Step Solution:

1. **Understanding Mutually Exclusive Events**:
- Two events are said to be mutually exclusive if they cannot occur at the same time. For example, if event A occurs, event B cannot occur, and vice versa.

2. **Understanding Non-Zero Probabilities**:
- The question specifies that the events have non-zero probabilities. This means that both events A and B have a probability greater than zero of occurring.

3. **Understanding Independent Events**:
- Two events are independent if the occurrence of one event does not affect the occurrence of the other. In mathematical terms, events A and B are independent if \( P(A \cap B) = P(A) \times P(B) \).

4. **Analyzing the Relationship**:
- If two events A and B are mutually exclusive and both have non-zero probabilities, then if one event occurs, the probability of the other event occurring becomes zero. This indicates that they cannot be independent.

5. **Conclusion**:
- Therefore, the statement can be completed as: "Two mutually exclusive events having non-zero probabilities of occurrence cannot be **independent**."

### Final Answer:
Two mutually exclusive events having non-zero probabilities of occurrence cannot be **independent**.