From genetics, we know that,
Human blood grouping is an example of multiple allelism as it is controlled by 3 alleles which are IAIB and i allele. The IAIB alleles are equally dominant over each other while i allele is recessive.
So, the child having blood group will necessarily have genotype ii.
Father probable genotype for blood group A: IAIA or IAi
Mother probable genotype for blood group B: IBIB or IBi
Now the following crosses can happen :
1) If both father and mother will be homozygous dominant then the gamete formation by father and mother will be IA and IB respectively - this will result in formation of a zygote of genotype IAIB which will give birth to a child with blood group AB - which is not asked in question.
2) If Father is homozygous and mother is heterozygous then by the same process as described above the blood group outcome of a child will be either AB(IAIB) or A(IAi). again which is not asked in the question.
3) If the father is heterozygous and mother is homozygous then by the same process as described above the blood group outcome of a child will be either AB(IAIB) or B(IBi), again which is not required.
4) If father and mother both are heterozygous then by the same process as described above the blood group outcome of a child will be O (ii). which is expected in the child from the question.
So, the correct genotype of father and mother will be IAi and IBi respectively while that of a child will be ii.