A' writes a letter to his friend B and oes not receive a reply, it is known that one out of 'n' letters does not reach it's destination. What is the probability that 'B' didn't receive the letter ? It is certain that 'B' would have replied , if he received the letter.

Answer

To solve the problem, we need to determine the probability that 'B' did not receive the letter given that 'A' did not receive a reply. We know that 1 out of 'n' letters does not reach its destination.

### Step-by-Step Solution:

1. **Define Events**:
- Let \( E \) be the event that 'B' received the letter.
- Let \( R \) be the event that 'A' received a reply from 'B'.

2. **Calculate Probability of Event \( E \)**:
- Since 1 out of \( n \) letters does not reach its destination, the probability that 'B' received the letter is:
\[ P(E) = \frac{n-1}{n} \]
- Therefore, the probability that 'B' did not receive the letter (complement of \( E \)) is:
\[ P(E') = 1 - P(E) = \frac{1}{n} \]

3. **Conditional Probability of Event \( R \) given \( E \)**:
- If 'B' received the letter, he would certainly reply. Hence:
\[ P(R|E) = 1 \]
- If 'B' did not receive the letter, he cannot reply, so:
\[ P(R|E') = 0 \]

4. **Calculate Probability of Event \( R \)**:
- Using the law of total probability:
\[ P(R) = P(R|E) \cdot P(E) + P(R|E') \cdot P(E') \]
- Substituting the known values:
\[ P(R) = (1) \cdot \left(\frac{n-1}{n}\right) + (0) \cdot \left(\frac{1}{n}\right) = \frac{n-1}{n} \]

5. **Find the Required Probability**:
- We want to find the probability that 'B' did not receive the letter given that 'A' did not receive a reply:
\[ P(E'|R') = \frac{P(E' \cap R')}{P(R')} \]
- First, calculate \( P(R') \):
\[ P(R') = 1 - P(R) = 1 - \frac{n-1}{n} = \frac{1}{n} \]
- Now, calculate \( P(E' \cap R') \):
- Since if 'B' did not receive the letter, 'A' cannot receive a reply:
\[ P(E' \cap R') = P(E') = \frac{1}{n} \]

6. **Final Calculation**:
- Now substituting back into the equation:
\[ P(E'|R') = \frac{P(E' \cap R')}{P(R')} = \frac{\frac{1}{n}}{\frac{1}{n}} = 1 \]

### Conclusion:
The probability that 'B' did not receive the letter given that 'A' did not receive a reply is \( 1 \).