Final answer:
The correct genotype for the dogs carrying the gene for deafness but having a normal hearing is 'Aa', indicating they are carriers and heterozygous. Autosomal recessive disorders require two copies of the recessive allele to manifest, and breeding two 'Aa' heterozygous carriers results in a 25% chance of an 'aa' offspring.
Step-by-step explanation:
The correct genotype for each of the dogs, who are carriers of the gene for deafness but have normal hearing, would be heterozygous for the deafness allele. This means that each dog must have one dominant allele for normal hearing and one recessive allele for deafness. The genotype for each dog is therefore 'Aa'. A dog with the genotype 'aa' would be deaf, while a dog with the genotype 'AA' would have normal hearing and not be a carrier of the deafness gene.
Autosomal recessive disorders, such as the type of deafness mentioned, only appear when an individual has two copies of the recessive allele. Since these two dogs have normal hearing, they cannot be 'aa' but must be carriers of the gene, meaning their genotype is 'Aa'. When two 'Aa' dogs are mated, there is a 25% chance for the offspring to be 'aa' (deaf), a 50% chance to be 'Aa' (carrier), and a 25% chance to be 'AA' (not a carrier).
For example, in humans, if neither parent shows signs of an autosomal recessive disorder but they have a child who does, it confirms that both parents are carriers ('Aa'). Likewise, in dogs, carriers of recessive traits such as deafness, coat color, or other inherited conditions can be identified by analyzing the offspring's phenotypes and genotypes.