## Core Concept
The ABO blood group system is controlled by a single gene with three alleles: A, B, and O. The A and B alleles are codominant, while the O allele is recessive. The genotype of an individual determines their phenotype, which is the expressed blood group.

## Why the Correct Answer is Right
The father has blood group B, which means his genotype can be either BB or BO. The mother has blood group AB, indicating her genotype is AB. For the children, we need to consider the possible genotypes and phenotypes they can inherit. The father can contribute either a B or an O allele (if his genotype is BO), and the mother can contribute either an A or a B allele. Therefore, the possible genotypes and phenotypes of the children are:
- From father: B or O
- From mother: A or B
Possible combinations: AB, BB, AO, BO
Phenotypes: AB, B, A, B
So, children can have blood groups A, B, or AB. They are unlikely to have blood group O because for a child to have O blood group, they must inherit an O allele from both parents. The mother (AB) does not have an O allele to give, making it impossible for the children to be OO (blood group O).

## Why Each Wrong Option is Incorrect
**Option A:** A - This is a possible blood group for the children, as they can inherit the A allele from the mother and the O allele from the father (if he is BO).
**Option B:** B - This is also possible as both parents can contribute a B allele (from the father) or the mother can contribute her B allele.
**Option C:** AB - This is possible as the mother can contribute her A or B allele, and the father can contribute his B allele.

## Why Option D is Correct (Implicit)
**Option D:** O - This is not likely because, as explained, the mother does not have an O allele to pass on, which is necessary for a child to have blood group O.

## Clinical Pearl / High-Yield Fact
A key point to remember is that the ABO blood group system follows specific inheritance patterns. Blood group O can only occur if an individual is homozygous recessive (OO), meaning they must inherit an O allele from both parents. This fact is crucial for understanding paternity and transfusion medicine.

## Correct Answer: D. O