If `P(E) = 0.25`, What is the probability of not `E`.

Answer

To solve the problem of finding the probability of not event E (denoted as P(not E) or P(E̅)), given that P(E) = 0.25, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between P(E) and P(not E)**:
The probability of an event and the probability of its complement (not the event) always sum up to 1. This can be expressed mathematically as:
\[ P(E) + P(not E) = 1 \]

2. **Substitute the known value**:
We know that P(E) = 0.25. We can substitute this value into the equation:
\[ 0.25 + P(not E) = 1 \]

3. **Isolate P(not E)**:
To find P(not E), we need to isolate it on one side of the equation. We can do this by subtracting 0.25 from both sides:
\[ P(not E) = 1 - 0.25 \]

4. **Calculate the result**:
Now, we perform the subtraction:
\[ P(not E) = 0.75 \]

5. **Conclusion**:
Therefore, the probability of not E is:
\[ P(not E) = 0.75 \]

### Final Answer:
P(not E) = 0.75

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