Answer:
The phenotypic ratio of the cattle offsprings is as follows:
Red polled = 1/8
Red horned = 1/8
White polled = 1/8
White horned = 1/8
Roan polled = 2/8
Roan horned = 2/8
Step-by-step explanation:
This is a cross involving two genes; one coding for coat color and the other for horn in cattle. The alleles of the first gene (Red, R and White, W) are codominant i.e. will both be expressed in a heterozygous state (Roan, RW). The polled allele (P) is dominant over the horned allele (p) in the second gene.
According to the question, a roan cow that is heterozygous for the horned gene will have genotype, RWPp while a roan bull that is horned will have genotype, RWpp. Hence, in a cross between these two cattles, each parent will undergo meiosis to produce the following possible gamete combinations;
RWPp- RP, Rp, WP, Wp
RWpp- Rp, Rp, Wp, Wp
These gametes used in a punnet square (see attachment) will produce 16 possible offsprings with 6 distinct phenotypes. The phenotypes are:
Red polled (RRPp or RRPP) = 2/16 or 1/8
Red horned (RRpp) = 2/16 or 1/8
White polled (WWPP or WWPp) = 2/16 or 1/8
White horned (WWpp) = 2/16 or 1/8
Roan polled (RWPP or RWPp) = 4/16 or 2/8
Roan horned (RWpp) = 4/16 or 2/8