Lets start out with this.
For every trait, there are 2 genes that represent it, they are located at different Loci (or locations in the DNA)
For example, base color is located at one loci, dilution at another and spots at another, etc. There may be several different genes that might be found at each loci, or only a few. But there is only room for 2 gene at each loci in any one animal.
Homozygous (homo) means that 2 copies of the same gene are present at a given Loci.
Heterozygous (hetero) means that 1 copy of one gene (dominant) and 1 copy of another gene(recessive) are present at a given Loci.
Dominant means that a gene will cover up other genes, and that it only takes 1 copy of such a gene to express the appearance. A dominant gene is written as a capital letter (E)
Recessive means that a gene requires 2 copies of the same gene for the trait to be expressed. When only one copy of the gene is present it is 'hidden'. A recessive gene is written as a small letter (e)
For the sake of black and red...
Homo black is written as EE
Hetero black is written as Ee
and
Red is written as ee. Red is ALWAYS homo
Any animal that is red is HOMOZYGOUS for the red gene. Red is a recessive trait, that means that it will only show up when the animal carries 2 genes for red.
Black is a dominant color, this means that if an animal carries 1 gene for black, it will BE black. This is how you get red calves out of 2 black parents. Both parents are Heterozygous for black (and for red) each parent will pass on the black gene 50% of the time and the red gene 50% of the time. If they both happen to pass on the red gene at the same time, you will get a red calf. If they both pass on the black gene you get a homo black calf and if one passes on red and the other black, you get a heterozygous 'black' calf.
Here is how it works out by the numbers
Ee x Ee = EE, Ee, Ee, ee
EE = 25%
Ee = 50%
ee = 25%