To solve the problem, we need to determine the genotypes of the deaf parents given that all their children have normal hearing. We know that genes A (represented as P) and B (represented as Q) are necessary for normal hearing, and that both genes must be present in their dominant forms (capital P and capital Q) for the offspring to have normal hearing.
### Step-by-Step Solution:
1. **Understanding the Genes**:
- For normal hearing, an individual must have at least one dominant allele for both genes A (P) and B (Q).
- This means the genotypes that can express normal hearing are:
- Capital P (dominant) and capital Q (dominant)
- Possible combinations include:
- Capital P, Capital Q (normal hearing)
- Capital P, small q (normal hearing)
- small p, Capital Q (normal hearing)
2. **Analyzing the Parents**:
- Both parents are deaf, which means they must have the recessive genotype for both genes. Therefore, they cannot have any dominant alleles (capital P or capital Q).
- The only possible genotype for both parents that would result in them being deaf is:
- small p, small p (for gene A)
- small q, small q (for gene B)
3. **Children's Hearing**:
- The problem states that all children have normal hearing. This indicates that the parents must carry at least one dominant allele for each gene, despite being phenotypically deaf.
- The only way this can happen is if both parents are heterozygous for one gene while being homozygous recessive for the other gene.
4. **Determining the Genotypes**:
- The only combination that allows for normal hearing in the offspring while both parents are deaf is:
- Parent 1: small p, small p, capital Q, small q (heterozygous for gene B)
- Parent 2: small p, small p, capital Q, small q (heterozygous for gene B)
- This means that each parent can contribute a capital Q to the offspring, allowing for normal hearing.
5. **Conclusion**:
- The correct genotypes for the parents are:
- Parent 1: small p, small p, capital Q, small q
- Parent 2: small p, small p, capital Q, small q
### Final Answer:
The genotype of the parents is:
- Parent 1: small p, small p, capital Q, small q
- Parent 2: small p, small p, capital Q, small q
