A husband and wife appear in an interview for two vacancies in the same post .The probability of husband 's selection is 1/7 and that of wife's 1/5
What is the probability that both of them will be selected ?

Options

A. `(2)/(7)`
B. `(1)/(35)`
C. `(24)/(35)`
D. `(11)/(35)`

Answer

To find the probability that both the husband and wife will be selected for the vacancies, we can follow these steps:

### Step 1: Identify the probabilities
- The probability of the husband being selected (P(H)) = 1/7
- The probability of the wife being selected (P(W)) = 1/5

### Step 2: Calculate the probability of both being selected
To find the probability that both the husband and wife are selected, we multiply their individual probabilities together. This is because the selection of one does not affect the selection of the other (assuming independence).

\[ P(\text{Both}) = P(H) \times P(W) = \frac{1}{7} \times \frac{1}{5} \]

### Step 3: Perform the multiplication
Now we perform the multiplication:

\[ P(\text{Both}) = \frac{1 \times 1}{7 \times 5} = \frac{1}{35} \]

### Step 4: State the final answer
Thus, the probability that both the husband and wife will be selected is:

\[ \frac{1}{35} \]