Medical Genetics Chances of having a child with Down syndrome increase with the mother's age: a 35-year-old woman has a one in 350 chance of conceiving a child with Down syndrome. This chance increases to one in 110 by age 40 and one in 30 by age 45Medical Genetics Chances of having a child with Down syndrome increase with the mother's age: a 35-year-old woman has a one in 350 chance of conceiving a child with Down syndrome. This chance increases to one in 110 by age 40 and one in 30 by age 45