Final answer:
The likelihood of Kate and her new partner having a son with both sickle-cell anemia and hemophilia is 12.5%, while the likelihood of a daughter having both conditions is 0% because hemophilia is an X-linked recessive disease and the father does not carry the gene for it.
Step-by-step explanation:
To assess the likelihood of Kate and her new partner having a child with both sickle-cell anemia and hemophilia, we need to understand the modes of inheritance for both diseases. Sickle-cell anemia is an autosomal recessive disorder, which means that both parents must be carriers for the child to have a chance of inheriting the disease. Since Kate has a child with sickle-cell anemia, she must be a carrier. Her new partner has a sister with sickle-cell anemia and his parents do not have the disease, suggesting that he too is a carrier. Therefore, there is a 25% chance that their child will have sickle-cell anemia.
Hemophilia A is an X-linked recessive disorder. Kate's father has hemophilia, so she is a carrier of the disease. Since her new partner has no history of hemophilia in his family, the likelihood of their child having hemophilia depends on the child's sex. If they have a son, there is a 50% chance he will have hemophilia. For daughters, the chance is 0% because they would receive a normal Y chromosome from their father.
Considering both diseases, the probability of their son having both sickle-cell anemia and hemophilia is the product of the individual probabilities (12.5%) – that's a 25% chance for sickle cell multiplied by a 50% chance for hemophilia. However, their daughters cannot have hemophilia, thus the probability of a daughter with both conditions is 0%.