Black and white coloration in cows is dominant to brown and white. black and white cows were crossed over several years and the following progeny were produced: 8 black and white and 3 brown and white. what is the most probable genotype of each parent?

If we can treat "black and white" as a single allele that is dominant, let's call it B.
"Brown and white" as a recessive single allele can be called b.
Because offspring were both brown and black, we know both parents must have a b allele, and at least one must have a B allele.
If we complete a Punnett square for two heterozygous parents, we get results of 25% homozygous dominant (BB), 50% heterozygous (Bb), and 25% homozygous recessive (bb). In terms of physical gene expression, 75% of offspring would be black and white, and 25% brown and white. Looking at the results we have, 3 brown and white and 8 black and white, the results are very close to the results of crossing two heterozygotes: we have about 73% black and white (8/11) and about 27% brown and white (3/11). So, the most probable genotype for each parent was that each parent was a heterozygote, with a genotype of (Bb.)

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