A couple having daughters only is expecting sixth progeny. The chance of the progeny being a son is

Options

A. 0
B. `25%`
C. `50%`
D. `100%`

Answer

To solve the question regarding the probability of the sixth progeny being a son, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Genetics**:
- In humans, sex is determined by the combination of X and Y chromosomes. Females have two X chromosomes (XX), while males have one X and one Y chromosome (XY).
- During reproduction, the male contributes either an X or a Y chromosome, while the female always contributes an X chromosome.

2. **Gamete Formation**:
- The male produces two types of gametes: 50% carry an X chromosome and 50% carry a Y chromosome.
- The female, on the other hand, produces only one type of gamete, which carries an X chromosome.

3. **Fertilization Outcomes**:
- If the male's X gamete fertilizes the female's X gamete, the offspring will be female (XX).
- If the male's Y gamete fertilizes the female's X gamete, the offspring will be male (XY).

4. **Calculating the Probability**:
- Since there are two possible outcomes (XX or XY) and both outcomes are equally likely, the probability of having a son (XY) is 50%.
- This means that regardless of the previous progeny being daughters, the chance of the next child being a son remains 50%.

5. **Conclusion**:
- Therefore, the chance of the sixth progeny being a son is 50%.

### Final Answer:
The chance of the progeny being a son is **C) 50%**.

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