In holstein cattle, the allele for black hair color (b) is dominant over the allele for red hair color (b), and the allele for polled (p), or lacking horns, is dominant over the allele for having horns(p). what is the expected phenotypic ratio of the offspring of a bbpp × bbpp cross if these alleles sort independently? ††

I hope you meant, a cross between BbPp and BbPp, else for bbpp x bbpp, all the progeny will be bbpp.

We need to work out a Punnett square to determine the genotypes resulting from the cross between BbPp and BbPp. The dyhybrid cross results in 16 different genotypes, of which a few have the same phenotypes.

It can be seen that there are 4 different kinds of phenotypes present, in the ratio 9:3:3:1.

We assume that these genes assort independently, have no interaction between them, and express complete dominance. By crossing two dihybrid individuals, it is expected a phenotypic ratio of 9:3:3:1 of the progeny.

Available data:

Two diallelic genes involved in hair color and horns development

Gene for Hair color

Gene for horns development

We will assume that these genes assort independently and express complete dominance.  

Cross: bbpp × bbpp

F1) 100% bbpp  ⇒ red haired animals with horns

We will perform another cross, just in case, for you to know how to proceed in the presence of dominant and recessive alleles.

Cross:  Between two dihybrid individuals

Parentals)   BbPp    x    BbPp

Gametes) BP, Bp, bP, bp

                 BP, Bp, bP, bp

Punnett square)   BP         Bp          bP           bp

                 BP     BBPP     BBPp      BbPP     BbPp

                 Bp     BBPp     BBpp      BbPp     Bbpp

                 bP     BbPP      BbPp     bbPP      bbPp

                 bp     BbPp      Bbpp     bbPp      bbpp

F1) Genotypes

      Phenotypes

Note: The symbol - represents either a dominant or a recessive allele.

So, according to this last cross, the expected phenotypic ratio of the offspring is 9:3:3:1.

Related link:  link

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