ajay and his wife kajal , the probability of ajay 's section is `1/7` and theat of his wife kajal 's section is `1/5` . What is the probability that
atleast one of them will be selected ?

Options

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

Answer

To find the probability that at least one of Ajay or Kajal will be selected, we can use the complementary probability approach. Here’s how we can solve it step by step:

### Step 1: Identify the probabilities
- The probability of Ajay being selected (P(A)) = 1/7
- The probability of Kajal being selected (P(B)) = 1/5

### Step 2: Calculate the probabilities of not being selected
- The probability of Ajay not being selected (P(not A)) = 1 - P(A) = 1 - 1/7 = 6/7
- The probability of Kajal not being selected (P(not B)) = 1 - P(B) = 1 - 1/5 = 4/5

### Step 3: Calculate the probability that neither is selected
The probability that neither Ajay nor Kajal is selected is the product of their individual probabilities of not being selected:
\[ P(not A \text{ and } not B) = P(not A) \times P(not B) = \left(\frac{6}{7}\right) \times \left(\frac{4}{5}\right) \]

Calculating this:
\[ P(not A \text{ and } not B) = \frac{6 \times 4}{7 \times 5} = \frac{24}{35} \]

### Step 4: Calculate the probability that at least one is selected
The probability that at least one of them is selected is the complement of the probability that neither is selected:
\[ P(at \text{ least one selected}) = 1 - P(not A \text{ and } not B) = 1 - \frac{24}{35} \]

Calculating this:
\[ P(at \text{ least one selected}) = \frac{35}{35} - \frac{24}{35} = \frac{11}{35} \]

### Final Answer
Thus, the probability that at least one of Ajay or Kajal will be selected is:
\[ \frac{11}{35} \]