Final answer:
A woman whose brother had Duchenne muscular dystrophy and who had unaffected parents has a 50% chance of being a carrier for the disease since she could have inherited the recessive gene from her mother.
Step-by-step explanation:
In the context of X-linked recessive disorders such as Duchenne muscular dystrophy (MD), understanding inheritance patterns is crucial. For a woman with a brother who had MD but unaffected parents, there is a significant chance that she inherited a recessive gene linked to the disorder. Here's why: MD is a condition almost exclusively found in males because they have only one X chromosome. If a male has the defective gene on the X chromosome, he will exhibit symptoms of the disease since there is no second X chromosome to mask the effect of the recessive gene. On the other hand, females have two X chromosomes, so a defective gene on one X chromosome can be masked by a normal gene on the other, rendering the female a carrier who does not exhibit symptoms.
Since the woman's brother had MD, he must have inherited a defective X chromosome from one of his parents. Because neither parent exhibited symptoms, each parent likely had one normal and one defective gene on their respective X chromosomes, making the mother a carrier. When an unaffected carrier mother and a genotypically normal father conceive a daughter, there is a 50% probability that the daughter will inherit the defective gene from her mother, becoming a carrier. However, each daughter has an equally likely chance of inheriting the unaffected X chromosome.
Given this scenario, the woman in question would have a 50% chance of being a carrier for the disorder since she could have either received the defective X chromosome or the normal one from her mother. Thus, the correct answer to her probability of being a carrier is (c) 50%.