What are the chances of a person with this disease passing the disease to their offspring?

 If a couple has a child with Down’s Syndrome, the couples next child has a dramatically increased chance of acquiring the disorder. Most Down’s Syndrome patients do not reproduce once they reach adulthood, because most DS males are considered sterile, where the DS females are indeed fertile. In most cases, the disorder is not "passed on", although in certain rare types of DS, that can happen.