Final answer:
The parents' genotypes can be determined based on the blood types of their children: one parent has type B blood, and the other has type O blood.
Step-by-step explanation:
The parents' genotypes can be determined based on the blood types of their children. A woman with type B blood can be genotype IBi, as type B blood is controlled by the IB allele, and the i allele represents the absence of A or B antigens. Since she has siblings with type O blood and type A blood, her parents must each contribute an i allele, resulting in a genotype of ii for both parents. Therefore, the correct answer is B. One parent has type B, and the other has type O blood.