Probability of four son to a couple is :-

Options

A. `1/4`
B. `1/8`
C. `1/16`
D. `1/32`

Answer

To solve the problem of finding the probability of a couple having four sons, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Probability of Having a Son or Daughter:**
Each child born to a couple has a 50% chance of being a son and a 50% chance of being a daughter. This can be expressed as:
- Probability of having a son (P(S)) = 1/2
- Probability of having a daughter (P(D)) = 1/2

2. **Identifying the Scenario:**
We want to find the probability of having four sons in a row. Since each child's gender is independent of the others, we can multiply the probabilities of each event occurring.

3. **Calculating the Probability for Four Sons:**
The probability of having four sons (S1, S2, S3, S4) can be calculated as:
\[ P(4 \text{ sons}) = P(S1) \times P(S2) \times P(S3) \times P(S4) \]
Since each probability is 1/2, we have:
\[ P(4 \text{ sons}) = \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) \]

4. **Simplifying the Calculation:**
This can be simplified to:
\[ P(4 \text{ sons}) = \left(\frac{1}{2}\right)^4 = \frac{1}{16} \]

5. **Conclusion:**
Therefore, the probability of a couple having four sons is \( \frac{1}{16} \).

### Final Answer:
The correct answer is option C: \( \frac{1}{16} \).