If `P(A)=(1)/(5)` and `P(A-B)=(1)/(6)`, then `P(A nn B)`=_______.

Answer

To solve the problem, we need to find \( P(A \cap B) \) given \( P(A) = \frac{1}{5} \) and \( P(A - B) = \frac{1}{6} \).

### Step-by-Step Solution:

1. **Understanding the Given Information**:
- We know that \( P(A) = \frac{1}{5} \).
- \( P(A - B) \) represents the probability of event A occurring without event B. It is given as \( P(A - B) = \frac{1}{6} \).

2. **Using the Relationship Between Probabilities**:
- The relationship between these probabilities can be expressed as:
\[ P(A - B) = P(A) - P(A \cap B) \]
- Here, \( P(A \cap B) \) is the probability of both events A and B occurring.

3. **Substituting the Known Values**:
- We can substitute the known values into the equation:
\[ \frac{1}{6} = \frac{1}{5} - P(A \cap B) \]

4. **Rearranging the Equation**:
- Rearranging the equation to solve for \( P(A \cap B) \):
\[ P(A \cap B) = \frac{1}{5} - \frac{1}{6} \]

5. **Finding a Common Denominator**:
- The common denominator for 5 and 6 is 30. We can rewrite the fractions:
\[ P(A \cap B) = \frac{6}{30} - \frac{5}{30} \]

6. **Performing the Subtraction**:
- Now, we can subtract the fractions:
\[ P(A \cap B) = \frac{6 - 5}{30} = \frac{1}{30} \]

7. **Final Answer**:
- Therefore, the probability \( P(A \cap B) \) is:
\[ P(A \cap B) = \frac{1}{30} \]

### Summary:
The final answer is \( P(A \cap B) = \frac{1}{30} \).