Final answer:
The 14-year-old boy likely has hemophilia, an X-linked recessive disorder. His sister's child, if male, has a 50% chance of being affected. The best estimate for the risk that her child will have the disease is 1/4, based on the provided options.
Step-by-step explanation:
The 14-year-old boy mentioned in the question likely suffers from hemophilia, a genetic disorder that affects blood clotting. Hemophilia is an X-linked recessive condition, usually passed from carrier mothers to their sons. As the boy's sister is not affected, she must be a carrier (since her brother is affected, and the disorder is rare in females who would require two defective X chromosomes to have the disease). The risk for her child to have hemophilia depends on the child's sex. If the child is male, there is a 50% chance he will inherit the affected X chromosome from his mother. If the child is female, there is no chance of being affected, but a 50% chance of being a carrier. Since the sex of the child is unknown, the best estimate combines the risk for both potential sexes. The risk is therefore 25% (1/4) that the child will be affected if the child is male, and 0% if the child is female, averaging to an overall 12.5% risk. However, to answer the question with the options provided, the closest estimate given would theoretically be 1/4 or 25%, assuming we are considering the risk for any child she has, ignoring the fact that for daughters the risk is 0%.