Mendelian Genetics: Probability of Offspring Fur Color in Dogs
Understanding Mendelian Genetics in Relation to Offspring Fur Color
When we talk about Mendelian genetics in relation to the color of fur in dogs, it refers to the inheritance patterns of specific traits from parent dogs to their offspring. In this case, we are focusing on the dominant and recessive genes that determine whether a dog's fur will be black or white.
According to the given data, black fur is dominant to white fur in dogs. This means that if a dog carries one allele for black fur (B) and one allele for white fur (b), the black fur trait will be expressed.
Calculating the Probability of Various Offspring Combinations
a) All with black fur: As each pup is an independent event, the probability of an offspring being black is 0.75 (3 out of 4 possibilities). The likelihood of all six pups being black then is (0.75)^6 = about 0.18, or 18%.
b) Four with black fur and two with white fur: For this combination, we use binomial probability. The calculation involves determining the number of ways to choose 4 black pups out of 6, multiplying by the probability of black fur (0.75) and white fur (0.25) respectively. The probability of this combination is about 0.32, or 32%.
c) At least two of the pups having white fur: The probability of at least two pups having white fur is calculated by subtracting the probability of having none or only one white puppy from 1. This works out to be about 0.89 or 89%.
d) The firstborn pup with white fur, and among the remaining five pups, three with black and two with white fur: To determine this combination, we calculate the probability of the first pup having white fur (0.25), then the probability of choosing 3 black pups out of 5 remaining, and 2 white pups out of 2 remaining. The overall probability is about 0.10 or 10%.
Understanding the principles of Mendelian genetics and binomial probability helps us predict the potential outcomes of offspring characteristics based on the genetic traits of the parent dogs.