Final answer:
A woman who is a premutation carrier of FXS has a 50% chance of passing on FXS to her sons, since the disorder is X-linked recessive. Daughters have a 50% chance of being carriers but are typically not affected.
Step-by-step explanation:
The chances of producing offspring with Fragile X Syndrome (FXS) if a woman is a premutation carrier is based on X-linked recessive inheritance patterns. In the case of FXS, which is an X-linked disorder, a woman who is a carrier has a mutated gene on one of her X chromosomes. If she has a son, there is a 50% chance that he will inherit FXS because he will receive his mother's affected X chromosome and has no other X chromosome to offset the mutated gene (as men have XY chromosomes).
Daughters will have a 50% chance of being carriers since they will inherit one of their mother's X chromosomes, which may or may not have the premutation. However, they will generally not be affected by FXS as females have another X chromosome (XX) which typically compensates for the mutated gene.