Which genotype represents a female carrier of an X-linked trait?

A female carrier of an X-linked trait possesses one normal allele and one mutated allele on her X chromosomes. In genetic notation, this is often represented as X^A for the normal allele and X^a for the mutated allele.

In this case, the genotype X^AX^a indicates that the female has one X chromosome with the normal allele (X^A) and another X chromosome with the recessive mutated allele (X^a). This configuration is characteristic of a carrier, as she does not express the trait associated with the recessive allele due to the presence of the dominant normal allele.

The other options describe different genetic scenarios. For instance, X^AX^A represents a female who is homozygous for the normal trait and would not be a carrier. Similarly, X^aX^a signifies a female who is homozygous for the recessive trait and would express it. The genotype X^AY represents a male who has one normal X chromosome and a Y chromosome, which does not pertain to the concept of a carrier female for X-linked traits. Thus, the correct choice reflects the definition of a carrier in this context perfectly.