If genetic factors blended together like paint then they could not be separated again. The white-flowered phenotype would therefore not reappear in the F2 generation, and all the flowers would be purple or maybe light purple, not white.
There is a maximum of two alleles for a normal autosomal locus from a diploid individual. In the whole population, there can be essentially an unlimited number of different alleles; the limit being determined by the population size.
In the F1 generation, the genotype of all individuals will be Ww and all of the dogs will have wiry hair.
In the F2 generation, there would be an expected 3:1 ratio of wiry-haired to smooth-haired dogs.
Although it is expected that only one out of every four dogs in the F2 generation would have smooth hair, large deviations from this ratio are possible, especially with small sample sizes. These deviations are due to the random nature in which gametes combine to produce offspring. Another example of this would be the fairly common observation that in some human families, all of the offspring are either girls, or boys, even though the expected ratio of the sexes is essentially 1:1.
You could do a test cross, i.e., cross the wiry-haired dog to a homozygous recessive dog (ww). Based on the phenotypes among the offspring, you might be able to infer the genotype of the wiry-haired parent.
From the information provided, we cannot be certain which, if either, allele is wild-type. Generally, dominant alleles are wild-type, and abnormal or mutant alleles are recessive.
Even before the idea of a homozygous genotype had really been formulated, Mendel was still able to assume that he was working with parental lines that contained the genetic material for only one variant of a trait (e.g., EITHER green seeds or yellow seeds), because these lines were pure-breeding. Pure-breeding means that the phenotype doesn’t change over several generations of self-pollination. If the parental lines had not been pure-breeding, it would have been very hard to make certain key inferences, such as that the F1 generation could contain the genetic information for two variants of a trait, although only one variant was expressed. This inference led eventually to Mendel’s First Law.
Equal segregation of alleles occurs only in meiosis. Although mitosis does produce daughter cells that are genetically equal, there is no segregation (i.e., separation) of alleles during mitosis; each daughter cell contains both of the alleles that were originally present in the parent cell.