3. The ABO blood type is controlled by a single locus, called I, with alleles IA, IB, and IO.

These give rise to the blood type phenotypes, A, B, AB, and O.
a. Suppose that parents know their phenotypes: the father is type AB and the mother is type
O. What are the genotypes of these parents?
b. What are the possible blood type phenotypes among their children?
c. Suppose that the father is type A and the mother is type B, and we don’t have any data
about their genotypes. What are the possible blood types among their children?

a. Based on the information given, we can determine the genotypes of the parents. The father is type AB, which means he must have inherited one A allele (IA) from one parent and one B allele (IB) from the other parent. Therefore, the father's genotype is IAIB.

The mother is type O, which means she must have inherited two O alleles (IO) - one from each parent. Therefore, the mother's genotype is IOIO.

b. The possible blood type phenotypes among their children can be determined by combining the alleles from the parents. Since the father's genotype is IAIB and the mother's genotype is IOIO, there are four possible combinations when their alleles combine: IAIO, IAIO, IBIO, and IBIO.

These combinations will result in the following blood type phenotypes among their children:
- Type A (IAIO)
- Type A (IAIO)
- Type B (IBIO)
- Type B (IBIO)

c. In this case, since we don't have any data about the genotypes of the parents, we can only determine the possible blood types among their children based on the possible genotypes of the parents.
For the father, who is type A, he could have the genotype IAIA or IAIO.
For the mother, who is type B, she could have the genotype IBIB or IBIO.

By considering all possible combinations of the parents' genotypes, we end up with the following possibilities for the children's blood types:
- Type A (IAIA from the father and IBIB or IBIO from the mother)
- Type A (IAIO from the father and IBIB or IBIO from the mother)
- Type B (IBIB from the mother and IAIA or IAIO from the father)
- Type B (IBIO from the mother and IAIA or IAIO from the father)
- Type AB (IAIA from the father and IBIB from the mother)
- Type AB (IAIO from the father and IBIB from the mother)
- Type AB (IAIA from the father and IBIO from the mother)
- Type AB (IAIO from the father and IBIO from the mother)
- Type O (IAIO from the father and IOIO from the mother)
- Type O (IAIO from the father and IOIO from the mother)

Therefore, the possible blood types among their children are Type A, Type B, Type AB, and Type O.

To determine the genotypes of the parents in question, we need to understand the inheritance patterns of the ABO blood type system. The ABO blood type is controlled by a single locus with three alleles: IA, IB, and IO.

a. The father has blood type AB, which means he inherited one allele from each parent. Since he has both A and B antigens, his genotype must be heterozygous, IAIB.

The mother has blood type O, which means she does not have A or B antigens. The O blood type allele is recessive, so her genotype must be homozygous for the O allele, IOIO.

b. When it comes to determining the possible blood type phenotypes among their children, we can refer to Punnett squares. Since the father has the genotype IAIB (A, B) and the mother has the genotype IOIO (O, O), the possible combinations of alleles for their children are as follows:

- IAIO (A, O)
- IBIO (B, O)

Therefore, their children could have either blood type A or B, resulting in the possible blood type phenotypes of A and B.

c. For this scenario, where the father is type A and the mother is type B, we do not have any information about their genotypes. However, we can determine the possible blood types among their children based on the possible combinations of alleles.

The father's phenotype is type A, which can be the result of two possible genotypes: IAIA (homozygous type A) or IAIO (heterozygous type A).

The mother's phenotype is type B, which can also be the result of two possible genotypes: IBIB (homozygous type B) or IBIO (heterozygous type B).

Based on the possible genotypes for the parents, the following combinations are possible for their children:

- IAIA × IBIB: All children will have blood type AB.
- IAIA × IBIO: There is a 50% chance for the children to have blood type A and a 50% chance for them to have blood type AB.
- IAIO × IBIB: There is a 50% chance for the children to have blood type B and a 50% chance for them to have blood type AB.
- IAIO × IBIO: There is a 25% chance for the children to have blood type A, 25% chance for them to have blood type B, and a 50% chance for them to have blood type AB.

Therefore, the possible blood types among their children could be AB, A, B, or AB.