Final answer:
The offspring of a cross between a homozygous brown hair person and a heterozygous brown hair person will have the genotypes Bb and the phenotypes brown hair. In the F2 generation, the genotypic ratio will be 1 BB : 2 Bb : 1 bb, and the phenotypic ratio will be 3 brown hair : 1 red hair.
Step-by-step explanation:
The homozygous brown hair person will have the genotype BB, while the heterozygous brown hair person will have the genotype Bb.
In the cross between these two individuals, all of the offspring will be heterozygotes with the genotype Bb.
The phenotypes of the offspring will be brown hair, as brown hair is dominant over red hair.
If these heterozygous offspring are self-crossed, the resulting F2 offspring will have the genotypes BB, Bb, and bb, in a ratio of 1 BB : 2 Bb : 1 bb.
The phenotypic ratio of the F2 offspring will be 3 brown hair : 1 red hair.