If E is any event associated with an experiment then.

Options

A. `P(E ) le 0`
B. ` P(E ) ge 1`
C. `P(E ) ge 0`
D. ` 0 le P(E ) le 1`

Answer

To solve the question "If E is any event associated with an experiment, then...", we need to analyze the properties of probabilities associated with events.

### Step-by-Step Solution:

1. **Understanding Probability**:
- Probability is a measure of the likelihood that an event will occur. It ranges from 0 to 1, where 0 indicates that the event will not occur, and 1 indicates that the event is certain to occur.

2. **Identifying Event E**:
- The event E can be any event associated with an experiment. It could either be a sure event (which will definitely happen) or an impossible event (which will definitely not happen).

3. **Analyzing the Probability of Event E**:
- If E is a sure event, then the probability \( P(E) = 1 \).
- If E is an impossible event, then the probability \( P(E) = 0 \).
- If E is a possible event (neither sure nor impossible), the probability \( P(E) \) can take any value between 0 and 1.

4. **Evaluating the Options**:
- **Option 1**: Probability less than 0. (Incorrect, as probabilities cannot be negative)
- **Option 2**: Probability greater than 1. (Incorrect, as probabilities cannot exceed 1)
- **Option 3**: Probability of E is greater than or equal to 0. (Partially correct, but it could also be greater than 1, which is not possible)
- **Option 4**: Probability of E is between 0 and 1. (Correct, as it encompasses all possible values for the probability of event E)

5. **Conclusion**:
- The correct answer is **Option 4**: Probability of E is between 0 and 1.