Final answer:
The genotype of the black Labrador retriever parent is Bb (heterozygous), as this is required to produce a brown puppy when mated with a brown Labrador, which has a genotype of bb (homozygous recessive).
Step-by-step explanation:
In genetics, when analyzing the offspring from a cross between two individuals, we can often infer the genotypes of the parents based on the phenotypes of the offspring. In the case of Labrador retrievers and their coat color, we know that the allele for black coat color (B) is dominant to the allele for brown coat color (b).
Given that a black Labrador was mated with a brown one and the outcome was four black puppies and one brown, we can conclude that some of the black puppies must have inherited a b allele from the black parent in order to produce the brown offspring. As the black parent mated with a brown Labrador, which is homozygous recessive (bb), the only way to produce a brown puppy (bb) is if the black Labrador is heterozygous (Bb), not homozygous dominant (BB).
Since we are able to produce a brown puppy, the black parent must carry the recessive b allele. Therefore, the genotype of the black Labrador retriever parent is Bb (heterozygous). This result aligns with what we would expect based on Mendelian inheritance patterns.