A man of blood group A marries a woman of blood group B.

The parents. The child of group O is $ii$, so each parent carries $i$. The man is $I^Ai$ and the woman is $I^Bi$.

(a) The children. $I^Ai \times I^Bi$ gives $I^AI^B$, $I^Ai$, $I^Bi$ and $ii$, each with a chance of $\frac{1}{4}$: $4$ genotypes, and they are four different blood groups, AB, A, B and O.

(b) Group AB. Only $I^AI^B$: a chance of $\dfrac{1}{4} = 25\%$. Each child is a new event, so the first child's group does not change this.

(c) Two children of group O. $\dfrac{1}{4} \times \dfrac{1}{4} = \dfrac{1}{16} = 6.25\%$.

(d) Different from both parents. The parents are A and B. Children of group AB or O differ from both: $\dfrac{1}{4} + \dfrac{1}{4} = 50\%$.

(e) The population. Three alleles can be put together two at a time in $6$ ways: $I^AI^A$, $I^AI^B$, $I^Ai$, $I^BI^B$, $I^Bi$ and $ii$. These give $4$ blood groups: A, B, AB and O.