What is the probability of each of the following combinations of offspring when two heterozygous black dogs are mated?
The probability of a litter of six pups with four black fur and two white fur, resulting from two heterozygous black dogs mating, is 15/64. In the case of a first litter of six pups with four black fur and two white fur, followed by a second litter of seven pups with five black fur and two white fur, the combined probability is 315/8192.
Understanding Black Fur Inheritance in Dogs
Black Fur Dominance:
In dogs, black fur color is dominant to white, which means that if a dog carries a black fur allele, it will display black fur. On the other hand, if a dog carries a white fur allele, it will exhibit white fur.
Heterozygous Black Dogs:
The term "heterozygous" indicates that both parent dogs have one black fur allele and one white fur allele. When these dogs mate, their offspring can inherit various combinations of alleles.
Probability Calculations:
To determine the probability of specific offspring combinations, we use the principles of Mendelian genetics. A Punnett square is a helpful tool for calculating these probabilities.
Combination A:
For a litter of six pups with four black fur and two white fur, the possible genotypes are BB, BW, BW, and WW. The probability of each genotype is 1/4. By multiplying these probabilities together, we get 15/64.
Combination B:
For the first litter of six pups with four black fur and two white fur, the probability is 15/64. In the second litter of seven pups with five black fur and two white fur, the genotypes BB, BW, and WW have probabilities of 9/32, 3/32, and 1/32. Multiplying these probabilities together results in 315/8192.
By understanding the genetics of fur color inheritance in dogs and applying probability calculations, we can determine the likelihood of different offspring combinations when two heterozygous black dogs are mated.