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

A person with XP generally has a 50% chance for passing it down to their offspring. Whether or not it is passed down is depended on their mate's genes.

If the affected person reproduces with a person that has homozygous dominant genes, then there is a 0% chance that their off spring will inherit XP.

If the affected person reproduces with a person that has heterozygous genes, then the offspring has a 50% chance of inheriting XP.

If the affected person reproduces with a person that has homozygous recessive genes, then the offspring has a 100% chance of inheriting XP