If two events are independent , then

Options

A. they must be mutually exclusive
B. sum of their probability must be 1
C. (a) and (b) are both correct
D. none of the above is correct

Answer

To solve the question "If two events are independent, then:", we need to analyze the options provided and apply the definition of independent events in probability.

### Step-by-Step Solution:

1. **Understanding Independence of Events**:
- 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:
\[ P(A \cap B) = P(A) \times P(B) \]
- This means that the probability of both events occurring together is equal to the product of their individual probabilities.

2. **Analyzing the Options**:
- **Option A**: They must be mutually exclusive.
- Mutually exclusive events cannot occur at the same time (i.e., \(P(A \cap B) = 0\)). If A and B are mutually exclusive, then they cannot be independent unless one of them has a probability of zero. Therefore, this option is incorrect.

- **Option B**: Some of their probability must be one.
- This statement is not necessarily true. The probabilities of independent events can be any value between 0 and 1, as long as they are not zero. Therefore, this option is also incorrect.

- **Option C**: A and B are both correct.
- Since both options A and B are incorrect, this option is also incorrect.

- **Option D**: None of the above is correct.
- Since options A, B, and C are all incorrect, this option must be correct.

3. **Conclusion**:
- Therefore, the correct answer is **Option D: None of the above is correct**.