What is the probability of three daughters to a couple in three children :-

Options

A. `1/4`
B. `1/8`
C. `1/16`
D. `3/8`

Answer

To solve the problem of finding the probability of a couple having three daughters when they have three children, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Probability of Having a Daughter**:
- When a couple has a child, the probability of having a daughter (D) is 1/2, and the probability of having a son (S) is also 1/2. This is because there are two possible outcomes for each child.

2. **Identifying the Total Outcomes for Three Children**:
- When the couple has three children, each child can either be a daughter or a son. Therefore, the total number of outcomes for three children can be calculated as:
\[ \text{Total outcomes} = 2^3 = 8 \]
- The possible combinations of children can be: DDD, DDS, DSD, DSS, SDD, SDS, SSD, SSS.

3. **Favorable Outcomes for Three Daughters**:
- The only favorable outcome for having three daughters is DDD. Thus, there is only 1 favorable outcome.

4. **Calculating the Probability**:
- The probability (P) of having three daughters can be calculated using the formula for probability:
\[ P(\text{3 daughters}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{1}{8} \]

5. **Conclusion**:
- Therefore, the probability of the couple having three daughters is \( \frac{1}{8} \).

### Final Answer:
The probability of a couple having three daughters when they have three children is \( \frac{1}{8} \).

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