Answer
The mother's genotype is A/O
The father's genotype is B/O
The first child's genotype is O/O
The second child's genotype is B/O
Work Step by Step
In the ABO blood group system there are three genes --A, B. and O. The A and B genes are codominant to each other, but they are dominant to the "O" gene. As a consequence, a person who has the "O" blood type must have the genotype O/O. However, an "A" blood type person may have the genotype A/A or A/O. Similarly, a person with blood phenotype "B" may have the genotype B/B or B/O.. For a child to be homozygous for the "O" gene he/she must receive an "O" gene from each parent . Since the mother has blood type "A" she must have the genotype A/O. The father could be O/O, but the second child has blood type "B". Since the only possible source of the "B" gene is the father, therefore, the father must have the genotype B/O.