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When trying to predict the outcome of genetic crosses, a Punnett square is a helpful tool. It's a grid that allows you to visualize and organize all the possible combinations of alleles that offspring can inherit from their parents.
The Punnett square consists of two axes: one representing the possible gametes (sex cells) from one parent, and the other representing the possible gametes from the other parent. Each square within the grid shows a potential genotype for an offspring.
For example, in our exercise, Parent 1 (genotype: \(aaBb\)) can produce gametes \(aB\) and \(ab\). Parent 2 (genotype: \(Aabb\)) can produce gametes \(Ab\) and \(ab\). By filling in the grid, we get different combinations of genotypes: \(AaBb\), \(Aabb\), \(aaBb\), and \(aabb\).
From this final Punnett square, you can easily see and calculate the percentage of certain traits—such as deafness in this case—by identifying which genotypes carry specific alleles, like allele \(B\), responsible for certain characteristics.

Alleles are different versions of a gene that can exist at a specific spot on a chromosome. Each individual has two alleles for each gene, one inherited from each parent. These alleles can be either dominant or recessive, which affects how traits and characteristics are expressed in an individual.
In the given exercise, we deal with two different traits controlled by alleles at two separate loci: one allele (\(A\)) is dominant and necessary for hearing, while the other allele (\(B\)) is dominant and can cause deafness regardless of the presence of allele \(A\). This explains why offspring with the genotype involving \(B\) (like \(AaBb\) or \(aaBb\)) will be deaf.
Using this understanding of alleles, it's possible to calculate the likelihood of any combination of traits appearing in offspring. The exercise demonstrates the power of specific dominant alleles (like \(B\)) to overrule other genetic factors.

Mendelian inheritance is the set of primary principles of genetics first described by Gregor Mendel in the 19th century. These principles explain how traits are passed from parents to offspring through generations. The key ideas include the existence of dominant and recessive alleles, how they segregate, and how they independently assort during gamete formation.
In this exercise, we witness Mendel's law of independent assortment in action. Alleles \(A\) and \(a\), and \(B\) and \(b\) are on different chromosomes, so they assort independently of each other. This means the inheritance of one pair of alleles (like \(A\) or \(a\)) doesn't affect the inheritance of another pair (like \(B\) or \(b\)).
The combination of these alleles in the offspring, as calculated by our Punnett square, leads to a variety of genotypes predicting the traits based on Mendel's laws. Understanding these basic principles helps you understand more complex genetic scenarios, such as those that might involve multiple genes contributing to a single trait.