Final answer:
The inheritance pattern is incomplete dominance, where neither the black nor white feather color is completely dominant, resulting in grey feathers in the heterozygous offspring of a mated rooster and hen with grey feathers.
Step-by-step explanation:
The pattern of inheritance described when a rooster with grey feathers is mated with a hen with grey feathers, resulting in offspring with grey, black, and white feathers, is incomplete dominance. In incomplete dominance, neither allele is completely dominant over the other, and the heterozygous phenotype is a blend of the two homozygous phenotypes. This is supported by the presence of three different feather colors in the offspring, which indicates that neither the black nor the white color is completely dominant. Instead, grey is the result of the incomplete dominance of the black and white alleles when combined in the offspring.