Consider the following statements:
1. If A and B are mutually exclusive events, then it is possible that `P(A)=P(B) =0.6`
II. If A and B are any two events such that `P(A//B) =1`, then `P(barB//barA) = 1`. which of the above statement is/are corrects?

Options

A. 1 only
B. 2 only
C. both 1 and 2
D. Neither 1 nor 2

Answer

To solve the problem, we need to analyze both statements provided in the question.

### Statement 1:
**If A and B are mutually exclusive events, then it is possible that `P(A) = P(B) = 0.6`.**

1. **Understanding Mutually Exclusive Events**:
- Two events A and B are mutually exclusive if they cannot occur at the same time. This means that the probability of both A and B happening together is zero:
\[ P(A \cap B) = 0 \]

2. **Using the Probability Formula**:
- The probability of the union of two mutually exclusive events is given by:
\[ P(A \cup B) = P(A) + P(B) \]
- If we substitute the values given in the statement:
\[ P(A) = 0.6 \quad \text{and} \quad P(B) = 0.6 \]
- Therefore:
\[ P(A \cup B) = 0.6 + 0.6 = 1.2 \]

3. **Conclusion for Statement 1**:
- Since probabilities cannot exceed 1, having \( P(A \cup B) = 1.2 \) is not possible.
- Thus, **Statement 1 is incorrect**.

### Statement 2:
**If A and B are any two events such that `P(A|B) = 1`, then `P(¬B|¬A) = 1`.**

1. **Understanding Conditional Probability**:
- The statement \( P(A|B) = 1 \) means that if event B occurs, event A must also occur. This implies:
\[ P(A \cap B) = P(B) \]

2. **Using the Complement Rule**:
- We need to show that \( P(¬B|¬A) = 1 \). This means that if A does not occur, then B also does not occur.
- According to the definition of conditional probability:
\[ P(¬B|¬A) = \frac{P(¬B \cap ¬A)}{P(¬A)} \]

3. **Relating the Events**:
- Since \( P(A|B) = 1 \), it follows that if A does not happen, B cannot happen either. Therefore:
\[ P(¬B \cap ¬A) = P(¬A) \]
- This leads us to:
\[ P(¬B|¬A) = \frac{P(¬A)}{P(¬A)} = 1 \]

4. **Conclusion for Statement 2**:
- Therefore, **Statement 2 is correct**.

### Final Conclusion:
- **Statement 1 is incorrect**.
- **Statement 2 is correct**.

Thus, the correct answer is that only Statement II is correct.