Final answer:
The primary risk factor for having a child with Down syndrome is the age of the mother, especially when the mother is over 35 years old, due to increased chances of chromosomal nondisjunction events.
Step-by-step explanation:
Risk factors for Down syndrome primarily include the age of the mother at the time of pregnancy. Specifically, pregnancy in women over age 35 is a significant risk factor. As women age, the likelihood of chromosomal nondisjunction during meiosis increases, leading to a higher probability of having a child with Down syndrome. This chromosomal error results in an extra copy of chromosome 21, a condition known as trisomy 21. The age of the father is less influential because nondisjunction events in sperm are much rarer than in eggs.
Regarding the options provided, the clear risk factor is pregnancy in women over age 35. The other proposed risk factors, such as fetal exposure to mutagens, increased paternal age, and family history of Down syndrome, do not have the same clear and direct correlation with the likelihood of having a child with Down syndrome as maternal age does. Current data indicates that the incidence of trisomy 21 increases dramatically with maternal age, particularly after the mother reaches 35 years of age.