Children in a family have blood type O, A, AB and B respectively.
What are the genotypes of their parents.

Options

A. `I^(A)i` and `I^(B)i`
B. `I^(A)I^(B)` and ii
C. `I^(B)I^(B)` and `I^(A)I^(A)`
D. `I^(A)I^(A)` and `I^(B)i`

Answer

To determine the genotypes of the parents based on the blood types of their children (O, A, AB, and B), we need to analyze the inheritance of blood types in humans.

### Step-by-Step Solution:

1. **Understand Blood Group Inheritance**:
- Human blood groups are determined by three alleles: IA (which produces blood type A), IB (which produces blood type B), and i (which produces blood type O).
- IA and IB are co-dominant, meaning that if both are present, the blood type will be AB. The i allele is recessive.

2. **Identify Possible Blood Types**:
- The blood types of the children are O, A, AB, and B.
- Blood type O can only be genotype ii.
- Blood type A can be either IAi or IAI.
- Blood type B can be either IBi or IBI.
- Blood type AB must be genotype IAIB.

3. **Determine Parent Genotypes**:
- Since one child has blood type O (genotype ii), at least one parent must contribute an i allele.
- The presence of AB (IAIB) indicates that one parent must have at least one IA and one IB allele.

4. **Construct Possible Parental Genotypes**:
- Let's assume the genotypes of the parents are IAi (A blood type) and IBi (B blood type).
- This combination allows for the following offspring:
- IAIB (AB)
- IAi (A)
- IBi (B)
- ii (O)

5. **Confirm Offspring Types**:
- From the cross between IAi and IBi, we can produce all four blood types:
- IAIB (AB)
- IAi (A)
- IBi (B)
- ii (O)
- This matches the blood types of the children given in the question.

6. **Conclusion**:
- Therefore, the genotypes of the parents must be IAi and IBi.

### Final Answer:
The genotypes of the parents are IAi (for blood type A) and IBi (for blood type B).

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