Events E and F are such that `P` (not E or not F) `=0.25`. State whether E and F are mutually exclusive.

Explanation

To determine whether events E and F are mutually exclusive given that \( P(\text{not } E \text{ or not } F) = 0.25 \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Given Probability**:
We are given that \( P(\text{not } E \text{ or not } F) = 0.25 \). This can be interpreted as the probability that at least one of the events E or F does not occur.

2. **Applying De Morgan's Law**:
According to De Morgan's Law, we can express the probability of the union of the complements:
\[ P(\text{not } E \text{ or not } F) = P(\text{not } (E \text{ and } F)) \]
Thus, we can rewrite the equation:
\[ P(\text{not } (E \text{ and } F)) = 0.25 \]

3. **Finding the Probability of the Intersection**:
The probability of the intersection of E and F can be found using the complement rule:
\[ P(E \text{ and } F) = 1 - P(\text{not } (E \text{ and } F)) \]
Substituting the value we have:
\[ P(E \text{ and } F) = 1 - 0.25 = 0.75 \]

4. **Determining Mutual Exclusivity**:
For events E and F to be mutually exclusive, the probability of their intersection must be zero:
\[ P(E \text{ and } F) = 0 \]
Since we found that \( P(E \text{ and } F) = 0.75 \), which is not equal to zero, we conclude that E and F are not mutually exclusive.

### Conclusion:
E and F are not mutually exclusive because \( P(E \text{ and } F) = 0.75 \), which is greater than zero.