Final answer:
The father's genotype for blood type is ii (type O), while the mother's genotype must be IBi since she has one child with type B blood and another with type O blood. Therefore, she must possess one B allele and one recessive i allele.
Step-by-step explanation:
Considering the children's blood types, and knowing the father is type O (genotype ii), we can infer the following about the genotypes of the parents:
- The father's genotype is ii, which indicates he has two recessive alleles since type O blood is recessive.
- Since one child is type B and one is type O, the mother must carry the allele for B (either IBIB or IBi).
- The child with type O blood indicates that the mother must have at least one 'i' allele (IBi).
- The mother cannot have the genotype IBIB because this would not allow the genotype ii (type O blood) in her offspring.
- Hence, the mother's genotype is IBi.
A type AB father and a type O mother could not have a type O child, since the child would receive either A or B allele from the AB parent, not allowing an ii genotype.