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

Carrier men pass the premutation to all their daughters but none of their sons. Each child of a carrier woman has a 50% chance of inheriting the gene. The Fragile X premutation can be passed silently down through generations in a family before a child is affected by the syndrome. A DNA blood test identifies both carriers and affected individuals.

Sources:
"What is Fragile X." Conquer Fragile X. 1 The National Fragile X Foundation. 4 Mar. 2009 <http://ww.fragilex.org/cfxf/about/php>.