To determine which allele combination represents a female who is a carrier for an X-linked recessive disorder, let's analyze the given options based on our understanding of genetics, particularly X-linked inheritance.
### Understanding X-Linked Recessive Disorders
1. X-linked Recessive Disorder:
- These disorders are caused by recessive alleles located on the X chromosome.
- Males (XY) have only one X chromosome, so a single recessive allele on the X chromosome will result in the disorder.
- Females (XX) have two X chromosomes, so they need two recessive alleles (one on each X chromosome) to express the disorder. If they have one dominant and one recessive allele, they are carriers.
2. Carrier Female:
- A carrier female has one normal (dominant) allele and one affected (recessive) allele. This means she does not show the disorder but can pass the affected allele to her offspring.
### Analyzing the Allele Combinations
Let's examine each provided allele combination:
1. Option 1: [tex]$x^R X^{\prime}$[/tex]
- Assuming [tex]$x^R$[/tex] represents the dominant allele and [tex]$X^{\prime}$[/tex] represents the recessive allele.
- This combination indicates one normal and one recessive allele, fitting the definition of a carrier female.
2. Option 2: [tex]$X^r X^r$[/tex]
- Both alleles are recessive.
- This combination represents a female with the disorder since both X chromosomes have the recessive allele.
3. Option 3: [tex]$X^{R Y}$[/tex]
- This represents a male where [tex]$X^R$[/tex] is the dominant allele and [tex]$Y$[/tex] is the Y chromosome.
- Males cannot be carriers of X-linked recessive disorders since they only have one X chromosome.
4. Option 4: [tex]$X^{\top} Y$[/tex]
- This combination is unusual and not typically used in standard genetic notation for describing X-linked disorders.
- We can consider this as an invalid or incorrect option.
### Conclusion
By analyzing each option, we determine that the combination which represents a female who is a carrier for an X-linked recessive disorder is:
- Option 1: [tex]$x^R X^{\prime}$[/tex]
Thus, the correct answer is:
[tex]\[
1
\][/tex]
