Black skin color is dominant to pink skin color in pigs. Two heterozygous black pigs are crossed.

If these pigs produce a total of three piglets, what is the probability that two will be pink and one will be black?

Verified step by step guidance

1. span>Step 1: Identify the genotypes of the parent pigs. Since black skin color is dominant and the pigs are heterozygous, their genotype is Bb, where B represents the dominant black allele and b represents the recessive pink allele.</span
2. span>Step 2: Determine the possible genotypes of the offspring using a Punnett square. Cross Bb (black) with Bb (black) to find the genotypic ratio of the offspring.</span
3. span>Step 3: Calculate the probability of each genotype. From the Punnett square, the genotypic ratio is 1 BB : 2 Bb : 1 bb. Therefore, the probability of a black piglet (BB or Bb) is 3/4, and the probability of a pink piglet (bb) is 1/4.</span
4. span>Step 4: Use the binomial probability formula to find the probability of having exactly two pink piglets and one black piglet. The formula is P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k)), where n is the total number of piglets, k is the number of pink piglets, p is the probability of a pink piglet, and C(n, k) is the binomial coefficient.</span
5. span>Step 5: Substitute the values into the formula: n = 3, k = 2, p = 1/4. Calculate the binomial coefficient C(3, 2) and substitute into the formula to find the probability.</span

Key Concepts

Mendelian Genetics

Mendelian genetics is the study of how traits are inherited through generations based on the principles established by Gregor Mendel. It involves understanding dominant and recessive alleles, where dominant alleles mask the expression of recessive ones. In this case, black skin color is dominant over pink, meaning that a pig with at least one black allele will exhibit black skin.

Punnett Square

A Punnett square is a diagram used to predict the genetic outcomes of a cross between two organisms. By organizing the alleles of the parents, it allows for the visualization of possible genotypes and phenotypes of the offspring. For the cross of two heterozygous black pigs (Bb x Bb), the Punnett square helps determine the probabilities of producing black and pink piglets.

Probability in Genetics

Probability in genetics refers to the likelihood of certain traits appearing in offspring based on parental genotypes. In this scenario, the probability of producing specific combinations of piglets can be calculated using the ratios derived from the Punnett square. For example, the likelihood of getting two pink and one black piglet from the total offspring can be determined using binomial probability formulas.