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. To determine the genotypes of the parents, we need to look at the possible combinations of alleles for each blood type phenotype.

For the father who is type AB, he has one allele for type A (IA) and one allele for type B (IB).

For the mother who is type O, she has two alleles for type O (IO).

So the genotypes of these parents are:

Father: IAIB
Mother: IOIO

b. To determine the possible blood type phenotypes among their children, we need to consider the possible combinations of alleles that can be passed on from each parent.

From the father, the possible alleles that can be passed on are IA and IB.
From the mother, the possible alleles that can be passed on are IO.

Using a Punnett Square, we can determine the potential blood type phenotypes of their children:

| I | O |
-----------------------------
I | IAIA | IAIO |
-----------------------------
O | IBIO | IOIO |

From the Punnett Square, we see that the potential blood type phenotypes among their children are:
- Type A (IAIA)
- Type B (IBIB)
- Type AB (IAIB)
- Type O (IOIO)

c. In this case, since we don't know the genotypes of the parents, we can't determine the exact blood types of their children with certainty. However, we can determine the possible blood types based on the possible combinations of alleles.

If the father is type A, he can have the following genotypes: IAIA or IAIO.
If the mother is type B, she can have the following genotypes: IBIB or IBIO.

Using a Punnett Square again, we can determine the potential blood type phenotypes of their children:

| I | I |
-----------------------------
I | IAIA | IAIB |
-----------------------------
I | IAIB | IBIB |

From the Punnett Square, we see that the potential blood type phenotypes among their children are:
- Type A (IAIA)
- Type B (IBIB)
- Type AB (IAIB)

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