A horticulturalist wants to produce geraniums with specific characteristics. She knows that the trait of red flowers is governed by the allele [tex]$R$[/tex] ([tex]$R R$[/tex] and [tex]$R r$[/tex]), and the trait of white flowers is governed by the allele [tex]$r$[/tex] ([tex]$r r$[/tex]).

The horticulturalist crosses two geraniums from the F1 generation. Look at the Punnett square to see this cross.

[tex]
\[
\begin{tabular}{|c|c|c|}
\hline
& R & r \\
\hline
R & R R & R r \\
\hline
R & R R & R r \\
\hline
\end{tabular}
\]
[/tex]

Which ratio of red-to-white flowering plants would she expect to see in the phenotypes of the F2 generation?

Certainly! Let's break down the genetics problem to determine the ratio of red-to-white flowering plants in the F2 generation based on the traits for flower color.

1. Understanding the Alleles:
- The allele [tex]$ R $[/tex] is for red flowers, and it can be either homozygous dominant (RR) or heterozygous (Rr) to produce red flowers.
- The allele [tex]$ r $[/tex] is recessive and results in white flowers when in the homozygous state (rr).

2. Setting Up the Cross:
- The horticulturalist is crossing two plants from the F1 generation. Each F1 plant is assumed to have the genotype Rr due to prior crosses resulting in all red flowers.

3. Using the Punnett Square:
- We draw a Punnett square to find out the possible offspring genotypes:

```
P1(Possible) | R | r
-------------------------
R | RR | Rr
-------------------------
r | Rr | rr
```

4. Analyzing Genotypes Produced:
- The Punnett square shows these possible genotypes for the offspring:
- [tex]$ RR $[/tex]: 1 occurrence
- [tex]$ Rr $[/tex]: 2 occurrences
- [tex]$ rr $[/tex]: 1 occurrence

5. Phenotypic Result:
- Both [tex]$ RR $[/tex] and [tex]$ Rr $[/tex] will result in red flowers because at least one dominant allele [tex]$ R $[/tex] is present.
- Only [tex]$ rr $[/tex] will produce white flowers.

6. Counting the Phenotypes:
- Red-flowering plants (both [tex]$ RR $[/tex] and [tex]$ Rr $[/tex]): Total of 3 occurrences.
- White-flowering plants ([tex]$ rr $[/tex]): Total of 1 occurrence.

7. Calculating the Ratio:
- The red-to-white flowering plants ratio is: [tex]$ 3:1 $[/tex].

So, the expected phenotypic ratio of red-to-white flowering plants in the F2 generation is [tex]$ 3:1 $[/tex].