The mother's genotype can be either [tex]X^AX^A[/tex] or [tex]X^AX^a[/tex].
For X-linked recessive traits, males (XY) can either be affected or free from the disorder, they cannot be carriers. Females (XX), on the other hand, can be affected, unaffected, or be carriers.
The circled male child is free from the disorder ([tex]X^AY[/tex]) while the females are carriers ([tex]X^AX^a[/tex]).
The male inherited the healthy allele, [tex]X^A[/tex], from the mother.
The female children inherit the affected allele from their father (who is affected for the disorder) and the other healthy allele from their mother.
This means that the mother cannot be affected for the disease. As it is, the pedigree points that all the children got their healthy alleles from their mother. This does not mean the mother has two healthy alleles though.
Thus, the possible genotype of the mother are [tex]X^AX^A[/tex] and [tex]X^AX^a[/tex].
More on pedigrees can be found here: https://brainly.com/question/2952835?referrer=searchResults