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. Step 1: Identify the genotypes of the parents. Since the pigs are heterozygous for black skin color, their genotype is Bb, where B represents the dominant allele for black skin and b represents the recessive allele for pink skin.
2. Step 2: Determine the possible offspring genotypes using a Punnett square. Cross Bb x Bb to find the probabilities of each genotype: BB (black), Bb (black), and bb (pink). The probabilities are 1/4 for BB, 1/2 for Bb, and 1/4 for bb.
3. Step 3: Calculate the probability of each piglet being pink (bb) or black (BB or Bb). The probability of a piglet being pink is 1/4, and the probability of being black is 3/4 (sum of BB and Bb probabilities).
4. Step 4: Use the binomial probability formula to calculate the probability of exactly two piglets being pink and one piglet being black. The formula is P(X=k) = (n choose k) * (p^k) * (q^(n-k)), where n is the total number of piglets (3), k is the number of pink piglets (2), p is the probability of a piglet being pink (1/4), and q is the probability of a piglet being black (3/4).
5. Step 5: Substitute the values into the binomial formula: P(X=2) = (3 choose 2) * (1/4)^2 * (3/4)^1. Simplify the expression to find the probability.

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 makeup of offspring from a particular cross. By arranging the alleles of the parents, it allows for the visualization of possible combinations in the offspring. For two heterozygous black pigs (Bb x Bb), the Punnett square helps determine the probabilities of producing black (BB or Bb) and pink (bb) 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 two pink and one black piglet from the total of three can be calculated using the binomial probability formula, considering the individual probabilities of each color from the Punnett square results.