A and B are two independent events such that `0 lt P(A) lt 1,0 < P(B) lt 1 ` then which of the following is not correct ?

Options

A. A and B are mutually exclusive
B. A' and B are independent
C. A and B' are independent
D. A' and B' are independent

Answer

To solve the problem, we need to analyze the properties of independent events and determine which statement about events A and B is not correct.

### Step-by-step Solution:

1. **Understanding Independence**:
- Two events A and B are said to be independent if the occurrence of one does not affect the occurrence of the other. Mathematically, this is expressed as:
\[ P(A \cap B) = P(A) \cdot P(B) \]

2. **Understanding Mutually Exclusive Events**:
- Events A and B are mutually exclusive if they cannot occur at the same time. This means:
\[ P(A \cap B) = 0 \]
- If A and B are independent, then they cannot be mutually exclusive unless one of the events has a probability of 0.

3. **Analyzing the Options**:
- We need to check the options provided in the question.
- Since A and B are independent and both have probabilities greater than 0 and less than 1, they cannot be mutually exclusive. Therefore, the statement "A and B are mutually exclusive" is incorrect.

4. **Checking Other Options**:
- For the other options, we check the independence of complements:
- \(A'\) (not A) and B are independent.
- A and \(B'\) (not B) are independent.
- \(A'\) and \(B'\) are independent.
- All these statements hold true due to the properties of independent events.

5. **Conclusion**:
- The only statement that is not correct is that A and B are mutually exclusive.

### Final Answer:
The statement that is not correct is: **A and B are mutually exclusive.**