If the dog with the unknown genotype is heterozygous, our cross would be: Aa x aa. In this model, A represents the dominant yellow-fur allele and a represents the recessive black-fur allele. We the black furred dog has to be genotype aa because he displays the recessive phenotype. The offspring produced from this cross would be 2 Aa and 2 aa genotypes, based on a punnet square.

This cross would generate offspring that are 50% Aa and 50% aa. This corresponds to 50% yellow and 50% black.

First, we need to find the genotype of the man. We know that his father has the disease, and that his mother is homozygous dominant. For his father to display the autosomal recessive trait, he must be homozygous recessive. We can thus write the man's parents' genotypes, using A as the dominant allele and a as the recessive allele.

Parents: AA (mother) x aa (father)

Offspring: All offspring will be Aa.

The man must inherit one allele from each parent, meaning he must be heterozygous.

This man, we are told, marries a heterozygous woman and they have a child. Again, we can write out this cross.

Man and woman: Aa (man) x Aa (woman)

Offspring: 1 AA (dominant), 2 Aa (dominant), 1 aa (recessive)

The possible offspring from this cross show a three-to-one ratio for displaying the dominant phenotype. Only one of the four possible offspring will be homozygous recessive and display the recessive phenotype. This one-in-four chance correspond to a 25% chance.

We know that the allele is autosomal, the father is heterozygous and black, and the mother is homozygous and white. From this information, we can determine that black must be dominant to white since the heterozygote shows the black phenotype. We will use B to represent the dominant black allele and b to represent the recessive white allele.

Cross: Bb x bb

Offspring: Half Bb (black) and half bb (white)

We can see that roughly half of the offspring will show the white phenotype. If there are twelve offspring, six of them will be white.

The first cross will produce a generation of double heterozygous flowers. Self-crossing this generation becomes a dihybrid cross problem.

In order to solve this problem, you can use either a punnett square and count the squares that display this phenotype, or you can use probability. Since purple is dominant, three out of four flowers will display the color purple. Since wrinkled is recessive to round, only one out of four flowers will display this phenotype. Since the flowers in question must express both of these traits, we can simply multiply these two fractions together.

You should be familiar with the 9:3:3:1 ratio of dihybrid cross phenotypes. A phenotype of one dominant trait and one recessive trait will always be observed with a  frequency.

Alleles are simply different versions of the same gene that encode for variations of the same characteristic. For example, different eye colors are encoded by different alleles of the same gene.   

Somatic cells in humans have two copies of each chromosome (2n=46) as opposed to haploid cells which have only one set of chromosomes (n=23). Muscle cells are somatic cells, sperm and ova are haploid cells, since they are gametes.  

A haploid cell is a cell that possesses only a single set of chromosomes (n=23) as opposed to the double set found in somatic cells (2n=46). The gametes (sperm and ova) in humans are examples of haploid cells. Also, the zygote is formed upon fusion of two gametes, and is thus diploid.    

Hybridization is the mating of two varieties of a species to produce hybrids. A classic example would be crossing purple flowered pea plants and white flowered pea plants. The resulting offspring would all be genetic hybrids in this case though they may only display one color.   

A genotype is the genetic makeup of alleles coding for a characteristic. In this example, a heterozygote has one recessive and one dominant allele, making the genotype Aa. The phenotype is the observable expression of the genotype. Since a heterozygote has one dominant allele and one recessive allele, the dominant allele is exhibited, thus the phenotype is brown hair.

The phenotype is the observable characteristic of an individual. In this example, a homozygous recessive plant will have a white flower phenotype and a genotype of aa.