Final answer:
To calculate the likelihood that exactly half the pups in a litter of six from two heterozygous dogs will have white fur, one needs to use a binomial probability formula considering the number of trials, the number of successes, and the probability of success for a single trial.
Step-by-step explanation:
The question is asking about the probability of a specific genetic outcome—in this case, the likelihood that half of the pups in a litter from two heterozygous dogs will have white fur. To solve this, we will use principles of Mendelian genetics and probability.
When two heterozygous individuals (Bb) are crossed, the Punnett square yields these possible genotypes for their offspring: BB, Bb, Bb, and bb. The phenotype resulting from BB or Bb will be brown fur, while bb will result in white fur. The probability of producing a white-furred pup (bb) from this cross is 1/4, since one of the four squares represents the bb genotype.
To determine the probability that exactly half of the six pups will be white, we must apply the binomial probability formula, which calculates the likelihood of a given number of successes (k) out of a fixed number of trials (n), given the success probability (p) for a single trial. In this case, n=6, k=3, and p=1/4.
The binomial probability formula is P(X = k) = (n! / (k! * (n - k)!)) * p^k * (1 - p)^(n-k). Substituting our values in, we get the probability that exactly three out of six pups will be white. However, it is important to note that without performing the actual calculation, it is not possible to provide the numerical probability.