For a child with Duchenne's muscular dystrophy, what is the chance that daughters will be carriers, and sons will develop the disease?

The situation described in the question pertains to genetic inheritance patterns, specifically X-linked recessive disorders such as Duchenne's muscular dystrophy, which typically affects boys more than girls. In this genetic model, the gene for Duchenne's muscular dystrophy is located on the X chromosome.

Since the mother has one X chromosome with the mutation (if she is a carrier) and the father has a Y chromosome (since it is a male), the inheritance patterns are as follows:

• Every daughter will inherit one X chromosome from their father (which will be Y-contingent and won't pass on the disease) and one X chromosome from their mother. Therefore, they have a 50% chance of inheriting the mutated X chromosome from their carrier mother, making them carriers themselves.

• Every son inherits their father's Y chromosome and one of the mother's X chromosomes. If the mother is a carrier, there is also a 50% chance that she will pass on the X chromosome with the mutation. If a son inherits the affected X chromosome, he will express the disease since he has no other X chromosome to compensate.

Therefore, the chance of daughters being carriers is indeed 50%, and the chance of sons developing the disease is also 50%.