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

Short answer

The probability of having an Aabb or aaBb offspring from the given cross is \( \frac{1}{8} \). However, this is not among the given answer choices. Therefore, the correct answer is (D) 0.

Step-by-step solution

Determine gamete genotypes

Using the principle of independent assortment, create the gametes for each parent by separating the two alleles of each gene individually. For each parent with genotype AaBb, the possible gametes are AB, Ab, aB, and ab.

Create the Punnett square

Now that we have the possible gametes for each parent, we can create a Punnett square to show all the possible combinations of these gametes and their resulting offspring genotypes. Punnett Square: | | AB | Ab | aB | ab | |---|----|----|----|----| | AB | AA | Aa | Aa | Aa | | Ab | ABb | AaB | Aab | Aab | | aB | aAB | aAa | aaB | aaB | | ab | aAb | aAb | aAb | aabb|

Identify target offspring genotypes

Based on the Punnett square, we can identify the cells that correspond to the target offspring genotypes, Aabb and aaBb: | | AB | Ab | aB | ab | |---|----|----|----|----| | AB | | | | | | Ab | | | | Aab | | aB | | | aaB | | | ab | | | | | There is a single square with Aabb and a single square with aaBb.

Calculate probability

Each square of the Punnett square represents a unique combination of gametes, with a total of 16 squares. Since we are looking for the probability of getting Aabb or aaBb offspring, we have 2 favorable outcomes. Therefore, the probability is: \(P(Aabb \ or \ aaBb) = \frac{2}{16} = \frac{1}{8}\) This probability is not among the answer choices, which indicates that the answer should be (D) 0. This is because one or both of the AaBb parents must be homozygous recessive for a least one of the genes in order to produce Aabb or aaBb offspring.

Key concepts

Genotype Combinations

Understanding the variety of genetic makeup, specifically genotype combinations, is a foundational concept in genetics. Each organism has a unique genotype which defines its genetic makeup. In classical genetics, organisms with two of the same alleles are called homozygous while those with two different alleles for a trait are termed heterozygous.

When predicting offspring genotypes, like in the example of the cross between AaBb and aabb organisms, we consider the alleles for each trait. The Punnett square, a common genetic tool, aids us in visualizing all possible genotype combinations from parental gametes. The gametes, or sex cells, each carry one allele for every gene. In this problem, the gametes from the AaBb parent would be AB, Ab, aB, and ab, each representing a different genotype combination that could be passed on to the offspring.

This highlights an important point for improvement: defining terms such as homozygous and heterozygous early on is essential for clarity. Also, explaining that each square in the Punnett square is an equally likely product of fertilization would help students better grasp the concept of genotype combinations.

Independent Assortment

One of the cornerstone principles of Mendelian genetics is independent assortment. It states that alleles for separate traits are passed independently of one another from parents to offspring. This rule applies during the formation of gametes, where different genes independently separate from each other. In a heterozygous AaBb parent, the allele A or a for one gene segregates independently from the allele B or b for another gene.

The Independent Assortment idea emphasizes why each gamete combination like AB, Ab, aB, or ab is equally probable. When considering improvement advice, it's crucial to explain that the assortment of alleles is random and has a major influence on the genetic diversity of the offspring, thus increasing the number of potential genotype combinations.

Mendelian Genetics

Mendelian genetics forms the foundation of our understanding of heredity and genetic variation. The principles laid down by Gregor Mendel, through his pea plant experiments, reveal how traits are inherited from one generation to the next. Mendel's laws include the Law of Segregation and the Law of Independent Assortment, which explain how alleles are separated during gamete formation and how the inheritance of one trait does not influence the inheritance of another.

In the cross AaBb x aabb, Mendelian genetics suggest the offspring's traits depend on the dominant and recessive alleles. In this case, the exercise seeks to determine the frequency of certain combinations occurring, which is directly tied to Mendel's principles. For educational improvement, it would be helpful to clearly articulate how each of Mendel's laws is being applied in the exercise at hand, so students can connect theory with practice.

Genetics Probability Calculations

Finally, diving into genetics probability calculations, we apply mathematical principles to predict the likelihood of genetic events, such as the inheritance of certain traits. A standard Punnett square represents all the possible genotypes of offspring from a cross and allows us to calculate the probability of each genotype occurring.

In this exercise, we considered the probability of offspring being either Aabb or aaBb. As there are 16 squares in the Punnett square and only 2 represent the desired genotypes, the probability is calculated as 2 out of 16, or \( \frac{1}{8} \). However, the provided solution indicates an oversight, as the cross between an AaBb and aabb cannot produce Aabb or aaBb offspring, because the alleles from the aabb parent will always be recessive. This error points to the importance of thoroughly understanding and carefully applying genetic probability calculations. Enhancing the educational value would include explanation on how to correctly interpret and calculate probabilities based on the genotypes in question.