In a family, father has a blood group 'A' and mother has a blood group 'B'. Their children show `50%` probability for a blood group 'AB' indication of that -

Options

A. Father is heterozygous
B. Mother is heterozygous
C. Either is heterozygous
D. Mother is homozygous

Answer

To solve the question regarding the blood groups of the parents and the probability of their children having blood group AB, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Possible Genotypes for Blood Groups**:
- The father has blood group A, which can be either genotype \( I^A I^A \) (homozygous) or \( I^A I^O \) (heterozygous).
- The mother has blood group B, which can be either genotype \( I^B I^B \) (homozygous) or \( I^B I^O \) (heterozygous).

2. **Set Up the Crosses**:
- If both parents are homozygous (father \( I^A I^A \) and mother \( I^B I^B \)), all children will have blood group AB (\( I^A I^B \)).
- If the father is heterozygous (\( I^A I^O \)) and the mother is homozygous (\( I^B I^B \)), the possible combinations for their children would be:
- \( I^A I^B \) (AB)
- \( I^A I^O \) (A)
- \( I^B I^O \) (B)
- This results in a 50% chance of having blood group AB.
- If the father is homozygous (\( I^A I^A \)) and the mother is heterozygous (\( I^B I^O \)), the possible combinations would be:
- \( I^A I^B \) (AB)
- \( I^A I^O \) (A)
- This also results in a 50% chance of having blood group AB.

3. **Conclusion**:
- Since the children show a 50% probability of having blood group AB, it indicates that at least one of the parents must be heterozygous. Therefore, the correct answer is that either the father or the mother is heterozygous.

### Final Answer:
The correct option is that either of the parents is heterozygous.

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