Alleles are defined as "alternative forms of a given gene."  Though Mendelian genetics tells us that the ideal model of a gene has only two alleles, dominant and recessive, we know this is not always the case, from things like codominance (blood type) and others. Some characteristics are defined by a combination of several alleles with varying weight of expression. Alleles on autosomes are inherited from both parents, but alleles in mitochondrial DNA are inherited from the mother only. Twins are an example of organisms with identical alleles, so the answers claiming that all organisms have different alleles is false.

The first generation shows an affected father and an unaffected mother. They produce both affected and unaffected children in the second generation, meaning that the disease cannot be recessive; if it were recessive, none of the second generation could be affected due to dominant alleles inherited from the mother. We can also conclude that the affected father is heterozygous.

Knowing that the trait is dominant, we must determine if it is autosomal or sex-linked. The trait can affect females, so it cannot be on the Y chromosome. The female in the second generation is affected, even though her mother is not, meaning she must be heterozygous. If the trait is on the X chromosome, it will be passed from the affected father to all female offspring, meaning that both females in the second generation would be affected. Because one female is not affected, she must have inherited an unaffected autosomal allele from the heterozygous father.

As such, the allele for the disease must be autosomal dominant.

If an autosomal trait skips a generation, it must be recessive; however, if an autosomal trait does not skip a generation, it can be either recessive or dominant.

These concepts can be easily seen when outlined via a pedigree analysis. A dominant trait cannot skip a generation; any presence of the allele will lead to expression, thus if the trait is not expressed in a given generation, it cannot be passed down (cannot skip). A recessive allele can be masked by carriers and reappear in a later generation.

Because males only have one X chromosome, while females have two, they are more likely to be affected by a problematic X chromosome. Females can mask recessive X-linked alleles as carriers; males will express all alleles on their singular X chromosome.

Males only pass on a Y chromosome to their sons, so it is impossible for them to pass an X-linked trait to a son. Furthermore, Y chromosomes are virtually free of contributing to inheritance-linked diseases.

If only males display the disorder, it is most likely a Y-linked genetic disorder. The only possible way to inherit this disease, then, would be through the inheritance of the father's Y-chromosome.

Women have two X-chromosomes, one from each parent, and could not possibly pass down the disorder.

Epigenetic inheritance could potentially explain a genetic disorder, but, if this were the case, it should not differentiate between males and females. Abnormal testosterone levels may be a result of the disorder, but they do no explain how the disorder is inherited.

Aneuploidy is a chromosomal condition in which there are an abnormal number of chromosomes in the cells of the body. Aneuploidy typically refers to monosomy (one chromosome copy) or trisomy (three chromosome copies), and arises due to nondisjunction during meiosis and gametogenesis. Nondisjuction causes one daughter cell to receive three or four chromatids, and the other to receive one or zero. If this gamete is used to form a zygote, all cells in the resulting offspring will carry the abnormal chromosome number.

Translocation occurs when chromosomal fragments join non-homologous chromosomes. Polyploidy is a condition in which a cell has more than two complete chromosomal sets; in this example, only one set of chromosomes carries three copies. Duplication is the presence of additional segments within a single chromosome.

X-linked disorders are inherited when a parent passes on his or her X-chromosome. Since females have two X-chromosomes, they are less likely to exhibit symptoms of a recessive disorder than males, who have only one. Females are capable of carrying a recessive X-linked trait without expressing it, while males are not. A male must inherit his Y-chromosome from the father and an X-chromosome from the mother, while a female must inherit X-chromosomes from both parents.

If a genotypically healthy mother and a colorblind father have a son, then this child must inherit an X-chromosome from the mother and a Y-chromosome from the father. The mother's chromosome are both genotypically normal, and do not possess the colorblind allele. This means that the son cannot possibly inherit a colorblind allele if the mother is genotypically normal.

All other presented answer represent scenarios that are possible.

The Punnett square below represents the couple's possible offspring, with the mother having genotype  and the father having genotype .

Since the disorder is X-linked, we know that any sons will necessarily inherit an affected allele from the mother. Any daughters will inherit an chromosome from each parent; by necessity, any daughters will be heterozygous carriers. The probability of any daughters being phenotypically normal is 100%, and the probability of any sons being colorblind is also 100%.

The question states that the couple had two sons and one daughter, and asks the probability that one son is colorblind, one son is normal, and one daughter is colorblind. These probabilities are 100%, 0%, and 100%, respectively.

There is a 0% chance that this combination of children is possible.

The first generation shows us a father with the disease and a mother without the disease. They produce three children, none of whom have the disease. Knowing that they do not have the disease allows us to eliminate dominant from consideration. In order for the third generation to be affected, the mother from the second generation must be a carrier. In the third generation, we see that the carrier mother has a male child with the disease with a father who does not have the disease. The male child will inherit the Y chromosome from his father, but must receive an X chromosome from the mother. He inherits the disease on this X chromosome.

Were the disease autosomal recessive, the father of the third generation child would need to be affected in order for him to inherit the trait. The disease must be X-linked recessive.

We know that red eyes are the dominant allele, which means white eyes are the recessive allele. Both sexes of offspring present the recessive allele. It is especially important to note that the daughters can express the recessive allele. This means that they must have inherited one recessive allele from each parent, while the sons must have inherited the recessive allele from the mother (they inherit the Y-chromosome from the father).

White-eye daughters: 

White-eye sons: 

Each parent must have at least one recessive, white-eye allele. Since the father has only one X-chromosome, this chromosome must carry the white eye allele. We know that they father must have white eyes.

Father: 

Since one parent has white eyes and the other has red eyes, we know the mother must have red eyes. She also carries the recessive allele, meaning that she is heterozygous.

Mother: 

From this cross, we are able to get the percentages reported in the question. 50% of daughters will have red eyes and 50% will have white. The same percentages will be seen for the sons.