To solve the question regarding which organism's female gametes determine the sex of the child, we will analyze the sex determination mechanisms in the given options: grasshopper, Drosophila, cockroach, and peacock.
### Step-by-Step Solution:
1. **Understand Sex Determination Mechanisms**:
- In many organisms, sex determination can be based on different chromosomal systems. The two most common systems are:
- **XX/XY system**: Typically, males are XY and females are XX.
- **ZW/ZZ system**: In this system, males are ZZ and females are ZW.
2. **Analyze Grasshopper**:
- In grasshoppers, the sex determination system is based on the XX/XY system.
- Males are X0 (having one X chromosome) and females are XX (having two X chromosomes).
- Here, it is the male gamete (X or O) that determines the sex of the offspring. Therefore, grasshoppers do not fit the criteria.
3. **Analyze Drosophila**:
- In Drosophila (fruit flies), the sex determination is also based on the XX/XY system.
- Males are XY and females are XX. Similar to grasshoppers, it is the male gamete that determines the sex of the offspring. Thus, Drosophila does not fit the criteria.
4. **Analyze Cockroach**:
- In cockroaches, the sex determination system is also XX/XY.
- Males are XY and females are XX. Again, the male gamete determines the sex of the offspring. Therefore, cockroaches do not fit the criteria.
5. **Analyze Peacock**:
- In peacocks, the sex determination system is based on the ZW/ZZ system.
- Males are ZZ and females are ZW. In this case, the female (ZW) produces two types of gametes: Z and W.
- The male (ZZ) produces only Z gametes. The sex of the offspring is determined by the type of gamete contributed by the female. If the female contributes a Z gamete, the offspring will be male (ZZ). If she contributes a W gamete, the offspring will be female (ZW).
- Therefore, in peacocks, it is indeed the female gamete that determines the sex of the child.
### Conclusion:
The correct answer is **peacock**, as the female gametes determine the sex of the child in this species.
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