**Core Concept**
The ABO blood group system and Rh blood type system are used to determine the compatibility of blood transfusions and the paternity of a child. In this scenario, we need to consider the possible genotypes of the mother and father based on their blood types to determine the likelihood of the child being their biological offspring.

**Why the Correct Answer is Right**
The mother has a blood type of A, which means she can be either AA or AO genotype. However, since the child is O, the mother cannot be AA genotype. Therefore, the mother's genotype is AO. The father has a blood type of B, which means he can be either BB or BO genotype. The child's blood type is O, which means the father must be BO genotype. The Rh blood type system also supports this conclusion, as the mother is Rh positive and the child is Rh negative, indicating that the father is likely the biological parent and is Rh positive.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because it does not take into account the child's blood type and the Rh blood type system.
**Option B:** This option is incorrect because it does not consider the possible genotypes of the mother and the Rh blood type system.
**Option C:** This option is incorrect because it is the opposite of the correct conclusion based on the ABO blood group system and Rh blood type system.

**Clinical Pearl / High-Yield Fact**
In cases where the mother and child have different blood types, it is essential to consider the possibility of a blood type mismatch and the implications for the child's health.

**Correct Answer:** C.