A man and his wife appear for an interview for two posts. The probability of the husband's selection is `1/7` and that of the wife’s selection is `1/5` . The probability that only one of them will be selected is

Options

A. `6/7`
B. `4/35`
C. `6/35`
D. `2/7`

Answer

To solve the problem, we need to find the probability that only one of the husband or wife is selected for the posts.

### Step-by-step Solution:

1. **Identify the probabilities:**
- Probability of the husband's selection, \( P(H) = \frac{1}{7} \)
- Probability of the wife's selection, \( P(W) = \frac{1}{5} \)

2. **Calculate the probabilities of not being selected:**
- Probability of the husband not being selected, \( P(H') = 1 - P(H) = 1 - \frac{1}{7} = \frac{6}{7} \)
- Probability of the wife not being selected, \( P(W') = 1 - P(W) = 1 - \frac{1}{5} = \frac{4}{5} \)

3. **Find the probability that only one of them is selected:**
- There are two scenarios where only one of them is selected:
1. The husband is selected and the wife is not selected.
2. The wife is selected and the husband is not selected.

- The probability for the first scenario (husband selected, wife not selected):
\[ P(H \cap W') = P(H) \times P(W') = \frac{1}{7} \times \frac{4}{5} = \frac{4}{35} \]

- The probability for the second scenario (wife selected, husband not selected):
\[ P(H' \cap W) = P(H') \times P(W) = \frac{6}{7} \times \frac{1}{5} = \frac{6}{35} \]

4. **Combine the probabilities of both scenarios:**
- The total probability that only one of them is selected is:
\[ P(\text{only one selected}) = P(H \cap W') + P(H' \cap W) = \frac{4}{35} + \frac{6}{35} = \frac{10}{35} = \frac{2}{7} \]

5. **Final Answer:**
- The probability that only one of them will be selected is \( \frac{2}{7} \).