A and B are two events such that` bar(A) and bar(B)` are mutually exclusive. If P(A)=0.5 and P(B)=0.6, then what is the value of `P(A|B)`?

Options

A. `(1)/(5)`
B. `(1)/(6)`
C. `(2)/(5)`
D. `(1)/(3)`

Explanation

To solve the problem, we need to find the conditional probability \( P(A|B) \) given that \( \bar{A} \) and \( \bar{B} \) are mutually exclusive, and we know \( P(A) = 0.5 \) and \( P(B) = 0.6 \).

### Step-by-Step Solution:

1. **Understanding Mutually Exclusive Events**:
Since \( \bar{A} \) and \( \bar{B} \) are mutually exclusive, it means that the events \( A \) and \( B \) cannot occur at the same time. Therefore, \( P(A \cap B) = 0 \).

2. **Using the Definition of Conditional Probability**:
The conditional probability \( P(A|B) \) is defined as:
\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]

3. **Substituting Known Values**:
From the previous step, we know that \( P(A \cap B) = 0 \). Thus, we can substitute this into the equation:
\[ P(A|B) = \frac{0}{P(B)} = \frac{0}{0.6} = 0 \]

4. **Conclusion**:
Therefore, the value of \( P(A|B) \) is \( 0 \).

### Final Answer:
\[ P(A|B) = 0 \]