In goats, the allele for black hair is dominant to that for red. Two black haired goats mated, producing twelve offspring. Of the first eleven, 8 had black hair and 3 had red hair. What is the probability of the twelfth offspring having red hair?
The data indicates that both parents are Br. The probability is the same as any goat for rr, 25%.
To determine the probability of the twelfth offspring having red hair, we need to consider the genotype of the parent goats and the inheritance pattern of the hair color in goats.
Since the allele for black hair is dominant to that for red hair, we can represent the genotypes of the parent goats as follows:
- Black-haired goat: BB (homozygous dominant)
- Red-haired goat: bb (homozygous recessive)
When these two goats mate, all their offspring will inherit one allele from each parent, resulting in a genotype combination of Bb (heterozygous genotype for hair color). In this case, the offspring will display the dominant trait, which is black hair.
Given that 8 out of 11 offspring have black hair and 3 have red hair, we can infer that there must be one Bb (heterozygous) offspring among the 12.
Therefore, the probability of the twelfth offspring having red hair is zero, as all available alleles from the parent goats have already been accounted for in the previous 11 offspring.