Final answer:
A 26-year-old woman likely carries a Robertsonian translocation involving chromosomes 14 and 21, which is the most probable explanation for having two children with Down syndrome and experiencing miscarriages.
Step-by-step explanation:
The best explanation for a 26-year-old woman who has produced two children with Down syndrome and has also had two miscarriages is likely due to a genetic anomaly involving her chromosomes. Option D: She carries a Robertsonian translocation involving chromosomes 14 and 21, is the most probable explanation. In this scenario, part of chromosome 21 is translocated to another chromosome, such as chromosome 14. This can lead to the offspring inheriting three copies of chromosome 21 when they receive the translocated chromosome along with two normal copies. The presence of three copies of chromosome 21 leads to Down syndrome, scientifically referred to as trisomy 21.
The relationship with a first cousin with Down syndrome (Option A) would not necessarily increase her risk unless there's a hereditary component, such as a Robertsonian translocation, which is not mentioned in the option. The age of the woman's husband (Option B) is unlikely to contribute significantly as nondisjunction events in sperm are less likely. Exposure to x-rays as a child (Option E) has not been proven to increase the risk of having children with Down syndrome. Miscarriages may also occur more frequently in pregnancies involving chromosomal abnormalities, which is consistent with the presence of a translocation