A woman with blood group A (heterozygous) and a man with blood group B (heterozygous) have children. What are the possible blood groups of their children?

Blood group A is represented by alleles I$^A$ and i. Since the woman has blood group A and is heterozygous, her genotype is I$^A$i.
Blood group B is represented by alleles I$^B$ and i. Since the man has blood group B and is heterozygous, his genotype is I$^B$i.

Parental genotypes: Woman (I$^A$i) $\times$ Man (I$^B$i)

The gametes produced by the woman are I$^A$ and i.
The gametes produced by the man are I$^B$ and i.

$$\begin{array}{|c|c|c|} \hline \text{Gametes} & \text{I}^A & \text{i} \\ \hline \text{I}^B & \text{I}^A\text{I}^B & \text{I}^B\text{i} \\ \hline \text{i} & \text{I}^A\text{i} & \text{ii} \\ \hline \end{array}$$

• I$^A$I$^B$: Blood group AB
• I$^B$i: Blood group B
• I$^A$i: Blood group A
• ii: Blood group O

The possible phenotypes arising in the children are:
$\boxed{\text{Blood group A, Blood group B, Blood group AB, Blood group O}}$