Explanation:

Blood groups are determined by the presence of certain antigens on the surface of red blood cells. There are four main blood types: A, B, AB, and O. Each blood type is determined by the combination of antigens inherited from both parents.

In this case, the father has blood group A and the mother has blood group B. The possible combinations of blood types that the children can inherit are as follows:

- Father's Blood Type: A
- Mother's Blood Type: B

Key Point 1: Inheritance of Blood Types

- Blood group A is determined by the presence of antigen A.
- Blood group B is determined by the presence of antigen B.
- Blood group AB is determined by the presence of both antigens A and B.
- Blood group O is determined by the absence of both antigens A and B.

Key Point 2: Punnett Square

To understand the probability of the children having blood group AB, we can use a Punnett square. Since the father has blood group A and the mother has blood group B, their genotypes can be represented as follows:

- Father's Genotype: AO
- Mother's Genotype: BO

The Punnett square for this cross would be:

```
| A | O |
----------------------
B | AB | OB |
----------------------
O | AO | OO |
----------------------

```

From the Punnett square, we can see that there are four possible combinations of genotypes for the children:

- AA: blood group A
- AO: blood group A
- BO: blood group B
- AB: blood group AB

Key Point 3: Probability of Blood Group AB

Out of the four possible combinations, only one combination (AB) results in blood group AB. Therefore, the probability of the children having blood group AB is 1 out of 4, which is 25%.

However, the question states that the children show 50% probability for blood group AB. This indicates that the parents are heterozygous for their respective blood types.

Conclusion:

Based on the given information, the correct answer is option 'C' - Either of the parent is heterozygous. This means that either the father or the mother has a genotype of AO or BO, which allows for the possibility of blood group AB in the children.