If `P(A nn B) = 0.15 . P(B) = 0.90` then `P(A//B)` is

Options

A. `(1)/(3)`
B. `(1)/(4)`
C. `(1)/(5)`
D. `(1)/(6)`

Answer

To find \( P(A | B) \), we can use the formula for conditional probability:

\[ P(A | B) = \frac{P(A \cap B)}{P(B)} \]

### Step-by-Step Solution:

1. **Identify the given values**:
- \( P(A \cap B) = 0.15 \)
- \( P(B) = 0.90 \)

2. **Substitute the values into the formula**:
\[ P(A | B) = \frac{P(A \cap B)}{P(B)} = \frac{0.15}{0.90} \]

3. **Simplify the fraction**:
- To simplify \( \frac{0.15}{0.90} \), we can divide both the numerator and the denominator by \( 0.15 \):
\[ P(A | B) = \frac{0.15 \div 0.15}{0.90 \div 0.15} = \frac{1}{6} \]

4. **Final answer**:
\[ P(A | B) = \frac{1}{6} \]