Determine the genotypes of the parents.

One parent has AB blood and the other has type B, but the children, 25% are type A, 25% are type AB, and 50% have type B blood.

To determine the genotypes of the parents, we need to analyze the blood types of the children. The possible genotypes for blood types are:

- A blood type: AA or AO
- B blood type: BB or BO
- AB blood type: AB
- O blood type: OO

Given that 25% of the children have type A blood, this means that one of the parents is a carrier of a recessive A allele (AO genotype) while the other parent has a B type allele (BB or BO genotype).
Similarly, since 50% of the children have type B blood, this means that both parents have at least one B allele.
Lastly, since 25% of the children have AB blood type, one of the parents must have an A allele and the other parent must have a B allele.

Combining this information, we can conclude that one parent has a B allele (BB or BO genotype) and the other parent has both an A allele and a B allele (AB genotype).