Problem 5 - AP Biology Premium Prep 2021

Question

Given the cross \(A a B b \times a a b b\), what is the probability of having an \(A a b b\) or aaBb offspring? (A) \(\frac{1}{2}\) (B) \(\frac{1}{4}\) (C) \(\frac{1}{16}\) (D) 0

Step-by-Step Solution

Answer

The short answer to the question is: (A) \(\frac{1}{2}\).

Step 1: Setup the Punnett square for Aa and aa alleles

To solve this problem, first, we will need to create the Punnett square for Aa (parent 1) and aa (parent 2). The Punnett square is a useful tool to visualize the possible offspring genotypes from a genetic cross. Aa | a A | a ----- a | a Here, the probabilities for each offspring genotype for the A locus are: - Aa: 50% (1/2) - aa: 50% (1/2)

Step 2: Setup the Punnett square for Bb and bb alleles

Similarly, construct the Punnett square for Bb (parent 1) and bb (parent 2). Bb | b B | b ----- b | b Here, the probabilities for each offspring genotype for the B locus are: - Bb: 50% (1/2) - bb: 50% (1/2)

Step 3: Calculate the probabilities for given offspring genotypes

Now, we will calculate the probabilities of the desired offspring genotypes Aabb and aaBb. To do this, we multiply the probabilities of each individual genotype for the two loci. Probability of Aabb offspring: - Aa (A locus): 50% (1/2) - bb (B locus): 50% (1/2) - Probability: (1/2) * (1/2) = (1/4) Probability of aaBb offspring: - aa (A locus): 50% (1/2) - Bb (B locus): 50% (1/2) - Probability: (1/2) * (1/2) = (1/4)

Step 4: Calculate the total probability

Finally, add the probabilities of the two offspring genotypes to find the overall probability. Total probability = Probability of Aabb offspring + Probability of aaBb offspring = (1/4) + (1/4) = (1/2) So the probability of getting an Aabb or aaBb offspring is (A) \(\frac{1}{2}\).