Offspring produced from a marriage have only O and A blood groups. The possible genotypes of the parents would be

Options

A. `I^(A)I^(A) " and " I^(A)I^(O)`
B. `I^(A)I^(A) " and " I^(O)I^(O)`
C. `I^(O)I^(O) " and " I^(O)I^(O)`
D. `I^(A)I^(O) "and " I^(O)I^(O)`

Answer

To determine the possible genotypes of the parents that can produce offspring with only O and A blood groups, we need to analyze the blood group inheritance based on the ABO blood group system.

### Step-by-Step Solution:

1. **Understanding Blood Groups and Genotypes**:
- The ABO blood group system has three alleles:
- \( I^A \) (A blood group)
- \( I^B \) (B blood group)
- \( I^O \) (O blood group)
- The blood group phenotypes are determined by the combinations of these alleles:
- Blood group A can have genotypes \( I^A I^A \) (homozygous) or \( I^A I^O \) (heterozygous).
- Blood group B can have genotypes \( I^B I^B \) or \( I^B I^O \).
- Blood group AB has the genotype \( I^A I^B \).
- Blood group O has the genotype \( I^O I^O \).

2. **Identifying Possible Offspring**:
- The offspring can only have blood groups A and O. Thus, the possible genotypes of the offspring must be \( I^A I^O \) (A blood group) and \( I^O I^O \) (O blood group).

3. **Analyzing Parent Genotypes**:
- We need to find combinations of parental genotypes that can produce the offspring blood groups of A and O.
- Let's evaluate the given options:

**Option 1**: \( I^A I^A \) and \( I^A I^O \)
- Possible offspring: \( I^A I^A \), \( I^A I^A \), \( I^A I^O \), \( I^A I^O \) (All offspring will be A blood group)

**Option 2**: \( I^A I^A \) and \( I^O I^O \)
- Possible offspring: \( I^A I^O \), \( I^A I^O \) (All offspring will be A blood group)

**Option 3**: \( I^O I^O \) and \( I^O I^O \)
- Possible offspring: \( I^O I^O \) (All offspring will be O blood group)

**Option 4**: \( I^A I^O \) and \( I^O I^O \)
- Possible offspring: \( I^A I^O \), \( I^O I^O \), \( I^O I^O \) (Offspring can be A or O blood group)

4. **Conclusion**:
- The only combination that allows for offspring with both A and O blood groups is from parents with genotypes \( I^A I^O \) and \( I^O I^O \). Therefore, the correct answer is:

**Possible genotypes of the parents: \( I^A I^O \) and \( I^O I^O \)**.