Final answer:
The fraction of the offspring that will be blue with a rose comb is 1/4 or 25%.
Step-by-step explanation:
In this case, the black chicken with a rose comb is homozygous for the coat color gene (BB) and dominant for the comb shape gene (RR). The splashed white chicken with a single comb is homozygous for the coat color gene (bb) and recessive for the comb shape gene (rr). When these two chickens are mated in the F2 generation, their offspring will inherit one gene for coat color and one gene for comb shape from each parent.
The possible genotypes of the offspring will be: BR, Bb, rR, and rr. However, only the genotype BbRr will result in a blue color with a rose comb. This means that 1 out of the 4 possible genotypes will produce the desired phenotype.
Therefore, the fraction of the offspring that will be blue with a rose comb is 1/4 or 25%.