If `P(E )=0.75`, what is the probability of 'not E'?

Answer

To find the probability of 'not E' given that \( P(E) = 0.75 \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Total Probability**: The total probability of all possible outcomes in a probability space is always equal to 1. This means that the probability of an event plus the probability of its complement (not the event) must equal 1.

\[ P(E) + P(\text{not } E) = 1 \]

2. **Identify the Given Probability**: We are given that \( P(E) = 0.75 \).

3. **Set Up the Equation**: We can express the probability of 'not E' as follows:

\[ P(\text{not } E) = 1 - P(E) \]

4. **Substitute the Given Value**: Now, substitute the value of \( P(E) \) into the equation:

\[ P(\text{not } E) = 1 - 0.75 \]

5. **Calculate the Probability**: Perform the subtraction:

\[ P(\text{not } E) = 0.25 \]

### Final Answer:
The probability of 'not E' is \( P(\text{not } E) = 0.25 \).

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