$A$ child has blood group $O$. If the father has blood group $A$ and mother has blood group $B$,work out the genotypes of the parents and the possible genotypes of the other offspring.

(N/A) The blood group characteristic in humans is controlled by three alleles,namely,$I^A$,$I^B$,and $i$. The alleles $I^A$ and $I^B$ are codominant,whereas allele $i$ is recessive to both. Individuals with genotypes $I^A I^A$ and $I^A i$ have blood group $A$,while individuals with genotypes $I^B I^B$ and $I^B i$ have blood group $B$. Persons with genotype $I^A I^B$ have blood group $AB$,and those with blood group $O$ have genotype $ii$.
Since the child has blood group $O$ (genotype $ii$),the child must have inherited one $i$ allele from each parent. Therefore,the parents must be heterozygous for their respective blood groups.
Father's genotype: $I^A i$ (Blood group $A$)
Mother's genotype: $I^B i$ (Blood group $B$)
When these parents are crossed:
Parents: $I^A i \times I^B i$
Gametes: $(I^A, i) \times (I^B, i)$
Possible genotypes of offspring:
$1$. $I^A I^B$ (Blood group $AB$)
$2$. $I^A i$ (Blood group $A$)
$3$. $I^B i$ (Blood group $B$)
$4$. $ii$ (Blood group $O$)
Thus,the other possible genotypes of the offspring are $I^A I^B$,$I^A i$,and $I^B i$.