Answer:
All white offspring: Parent 1 genotype = homozygous dominant 
                             Parent 2 genotype = homozygous/heterozygous dominant
For all black offspring: Parent 1 genotype = homozygous recessive
                                      Parent 2 genotype = homozygous recessive
Explanation:
The cross was between a white mouse and a black mouse and the phenotypic ratio of the resulting offspring is 50% white and 50% black.
Assuming that fur color in the mouse is represented by the allele A (a), In order to give 1:1 phenotypic ratio of the offspring, it means the white mouse is heterozygous with Aa genotype and the black mouse is homozygous with aa genotype. Also, it means that the allele A is dominant over the allele a.
                        Aa    x    aa
                  Aa    Aa    aa    aa
Aa = white
aa = black
Ratio of white to black = 50/50 or 1:1
Hence, in order for a cross to yield only white offspring, the parents can either be homozygous AA and AA or one will be homozygous AA and the other will be heterozygous Aa.
1.              AA    x    AA
        AA    AA    AA    AA (all white offspring)
2.            AA    x    Aa
         AA    Aa    AA    Aa (all white offspring).
In order to produce only black offspring, both parents must be homozygous aa.
              aa    x    aa
          aa    aa    aa    aa    (all black offspring)