Question

Given the cross \(A a B b C c \times A a B b C c\), what is the probability of having an \(A A B b C C\) offspring? (A) \(\frac{1}{4}\) (B) \(\frac{1}{8}\) (C) \(\frac{1}{16}\) (D) \(\frac{1}{32}\)

Short answer

The probability of having an \(A A B b C C\) offspring is \(\frac{1}{64}\), which is not among the given options.

Step-by-step solution

Probability for getting AA alleles

First, we examine the probability of obtaining AA alleles from the parents. Both parents have a heterozygous Aa genotype, which means they have a 50% chance of passing along the dominant A allele to their offspring. Since both parents contribute one allele, the probability of the offspring having AA genotype is: \((\frac{1}{2})^2 = \frac{1}{4}\)

Probability for getting BB alleles

Next, we analyze the probability of obtaining BB alleles from the parents. Since both parents have Bb genotype, the probability of the offspring inheriting B allele is 0.5 (50% chance from each parent). Therefore, the probability of the offspring having a BB genotype is: \((\frac{1}{2})^2 = \frac{1}{4}\)

Probability for getting CC alleles

Lastly, we determine the probability of obtaining CC alleles from the parents. Both parents have the Cc genotype, meaning there is a 50% chance of inheriting dominant C allele from each parent. So, the probability of the offspring having a CC genotype is: \((\frac{1}{2})^2 = \frac{1}{4}\)

Multiply individual probabilities

Now we need to multiply the probabilities for AA, BB, and CC to find out the overall probability of the offspring having AABBCC genotype. The probability is: \(\frac{1}{4}\times\frac{1}{4}\times\frac{1}{4} = \frac{1}{4^3} =\frac{1}{64}\) The correct answer is not one of the available options (A, B, C, or D). This means there might be an error in the given choices, or the problem might need revision.

Key concepts

Mendelian Genetics

Mendelian genetics is a set of primary principles that underpin the mode of inheritance for traits from parents to offspring. Named after Gregor Mendel, a pioneer in the study of heredity, these principles describe how the genetic information carried in genes is transmitted through gametes (sperm or egg cells) and how it manifests in subsequent generations.

There are three key laws of Mendelian genetics - the Law of Segregation, the Law of Independent Assortment, and the Law of Dominance. The Law of Segregation states that an individual inherits a pair of alleles (one from each parent) for a given trait, and these alleles separate during gamete formation. The Law of Independent Assortment explains how different genes independently separate from one another when reproductive cells develop. Lastly, the Law of Dominance states that some alleles are dominant and others are recessive; if an organism inherits a dominant allele, it will express the dominant trait.

Understanding these principles is crucial to predict and calculate genetic probabilities, which explain the likelihood of an offspring inheriting certain traits.

Genotypic Probability

Genotypic probability is the likelihood of offspring inheriting a particular set of alleles that make up its genotype. This concept is at the heart of predicting genetic outcomes for a variety of traits. The genotype refers to the genetic makeup of an individual organism and can include homozygous alleles (same alleles, like AA or aa) or heterozygous alleles (different alleles, like Aa).

In terms of calculations, we often utilize probability rules, such as the product rule, which states that the probability of two independent events both occurring is the product of their individual probabilities. When considering multiple traits, the genotypic probabilities for each trait are multiplied together to find the overall likelihood of a particular genetic outcome.

Punnett Square

A Punnett square is a graphical tool used in genetics to predict the genotypes of offspring from a particular cross between two parents. To create a Punnett square, we draw a grid and write one parent's possible gametes along the top and the other parent's possible gametes along the side. Each cell of the grid represents a potential offspring genotype.

The power of a Punnett square lies in its visual representation of all possible genetic combinations for offspring, given the parent genotypes. It's particularly useful for simple Mendelian genetics involving one or two traits. By filling in the grid, one can easily see the expected ratios of offspring genotypes. This helps in understanding how different allele combinations affect the probability of producing certain genotypes.

Heterozygous Genotype

A heterozygous genotype is characterized by an organism that has two different alleles for a specific gene - one inherited from each parent. For example, in a heterozygous genotype like Aa, A represents one allele and a represents the other. Heterozygosity is fundamental in predicting the variation in traits observed within a population since it enables the combination of both dominant and recessive alleles.

In our example, both parents have a heterozygous genotype (Aa Bb Cc), meaning that they have mixed alleles for each gene. As a result, offspring have a variety of possible genotypes based on the combinations of alleles they inherit. The concept of heterozygous genotypes allows us to calculate the probability of offspring having certain traits and understand the genetic diversity within generations.