Explanation:

Let’s analyze the problem step-by-step using given probabilities:

- Probability Kesari receives the letter: 9/10.

- Probability Kesari does not receive the letter: 1/10.

- Kesari will reply if he receives the letter.

Given Sanjay does not receive a reply, Kesari did not get the letter.

Using Bayes' theorem, calculate:

- Probability of not receiving a reply: \( P(\text{No Reply}) = P(\text{Kesari receives}) \times P(\text{No Reply}|\text{Receives}) + P(\text{Kesari does not receive}) \)

- \( P(\text{No Reply}) = (9/10) \times 0 + (1/10) = 1/10 \)

- Probability did not receive given no reply: \( \frac{1/10}{1/10} = 1 \)

Therefore, none of the options match. But to find the probability of not receiving the letter (if proposed options): It should be \( \frac{1/10}{(1 \times 9/10) + (1/10)} = \frac{1}{1.9} = \frac{10}{19} \).

Thus, Option 1 (10/19) is indeed the correct answer.