Given that `P(A) = 1//3, P(B) = 1//4, P(A//B) = 1//6`, then what is `P(B//A)` equal to ?

Options

A. `1//4`
B. `1//8`
C. `3//4`
D. `1//2`

Explanation

To solve the problem, we will use the formula for conditional probability and the information provided in the question.

### Step-by-Step Solution:

1. **Given Information:**
- \( P(A) = \frac{1}{3} \)
- \( P(B) = \frac{1}{4} \)
- \( P(A|B) = \frac{1}{6} \)

2. **Using the Formula for Conditional Probability:**
The formula for conditional probability is:
\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]
Rearranging this formula gives us:
\[ P(A \cap B) = P(A|B) \cdot P(B) \]

3. **Substituting the Values:**
Now, substituting the known values into the equation:
\[ P(A \cap B) = P(A|B) \cdot P(B) = \frac{1}{6} \cdot \frac{1}{4} \]
\[ P(A \cap B) = \frac{1}{24} \]

4. **Finding \( P(B|A) \):**
We need to find \( P(B|A) \), which is given by the formula:
\[ P(B|A) = \frac{P(B \cap A)}{P(A)} \]
Since \( P(B \cap A) = P(A \cap B) \), we can substitute:
\[ P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{1}{24}}{\frac{1}{3}} \]

5. **Calculating \( P(B|A) \):**
Simplifying the fraction:
\[ P(B|A) = \frac{1}{24} \cdot \frac{3}{1} = \frac{3}{24} = \frac{1}{8} \]

### Final Answer:
Thus, the probability \( P(B|A) \) is equal to \( \frac{1}{8} \).

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