**Core Concept**
The underlying principle being tested is the inheritance of **ABO blood groups**, which is determined by a single gene with three alleles: A, B, and O. The A and B alleles are codominant, while the O allele is recessive.

**Why the Correct Answer is Right**
Given the father has blood group B (can be BB or BO) and the mother has AB, the possible genotypes and phenotypes of the child can be determined. The mother can only contribute A or B alleles, and the father can contribute B or O alleles. Thus, the child can inherit A, B, or O from the parents, resulting in possible blood groups of A, B, or AB if the child inherits A or B, and O if the child inherits O from the father and O is not a possible allele from the mother.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because the child can inherit the A allele from the mother and the B allele from the father, resulting in an AB blood group.
**Option B:** This option is incorrect because the child can inherit the B allele from both parents, resulting in a B blood group.
**Option C:** This option is not provided, but based on the explanation, the child can also inherit the A allele from the mother and the O allele from the father, resulting in an A blood group.

**Clinical Pearl / High-Yield Fact**
It's crucial to remember that the O allele is recessive and will only express if an individual is OO. If a parent is AO or BO, they can still pass the O allele to their offspring, who may express it if they also inherit an O from the other parent.

**Correct Answer:** Correct Answer: D. O