Suppose a father of blood type A and a mother of blood type B have a child of type O. What types are possible in their subsequent children?

A child with blood type O must be homozygous for this trait. The only possible combination of genes that can produce blood type O is if an individual receives two O genes--one from each parent.
We already know that one parent is blood type A and the other is blood type B. Since the genes for type A and type B are co-dominant and the gene for type O is recessive, each parent must be heterozygous for blood type.
This implies that one parent has the gene combination AO and the other parent has the gene combination BO. In a Punnet square, there are four possible offspring that this couple could produce. AO which is type A, BO which is type B, AB which results in type AB or OO which results in type O.
Therefore, if this couple ever produces more offspring there is a 25% chance of producing each of the four blood types.
I have included a link which shows how the Punnett square is solved for this problem.