Final answer:
A mouse with black fur and red eyes could have the genotype BbRr, since it must have pigment production and no agouti allele present (option B).
Step-by-step explanation:
The question is regarding the genotype of a mouse with black fur and red eyes. Based on the given information that mottled agouti coat color (A) is dominant to solid black or gray and that a separate gene (C) is responsible for pigment production, where cc results in albinism, we can deduce the correct genotype.
For the mouse to have black fur, it must not be albino; thus, it must have at least one functional C allele. Since black is a solid color, the genotype must also not have the dominant A allele for agouti coloring. Therefore, the correct genotype must have at least one of the B alleles (which stands for black in this context) and at least one C allele.
So, the correct genotype for a mouse with black fur and red eyes would be BbRr, assuming that the B and R alleles are responsible for the observed phenotypes and are not linked to the A or C alleles discussed.
Therefore, the answer is option B.