Final answer:
To ensure all offspring have black coats when mated with a yellow lab (bbee), the other dog must have the genotype BBEE, which provides dominant E alleles to mask the yellow color and B alleles for a black coat.
Step-by-step explanation:
In Labrador retrievers, coat color is determined by two genes, B and E, where the presence of the E allele allows the B allele to be expressed, resulting in either black or brown coats. The question concerns the necessary genotype of a dog to ensure all black-coated offspring when mated with a yellow lab with the genotype bbee. Since the yellow lab provides an ee combination, which is epistatic to the B gene, the other parent must provide an E allele to override the yellow coat color.
The only genotype from the options listed that can provide dominant E alleles to all offspring is BBEE, as it ensures the presence of at least one E allele and at least one B allele in all the offspring for a black coat color. The yellow lab's b alleles are irrelevant since a single B allele is sufficient to result in a black coat when combined with an E allele.