Radishes may be long, round, or oval, and they may be red, white, or purple. You cross a long, white variety with a round, red one and obtain an oval, purple $\mathrm{F}_{1}$. The $\mathrm{F}_{2}$ shows nine phenotypic classes as follows: 9 long, red; 15 long, purple; 19 oval, red; 32 oval, purple; 8 long, white; 16 round, purple; 8 round, white; 16 oval, white; and 9 round, red.
a. Provide a genetic explanation of these results. Be sure to define the genotypes and show the constitution of the parents, the $\mathrm{F}_{1},$ and the $\mathrm{F}_{2}$
b. Predict the genotypic and phenotypic proportions in the progeny of a cross between a long, purple radish and an oval, purple one.