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]RR[/tex] and [tex]Rr[/tex]), and the trait of white flowers is governed by the allele [tex]r[/tex] ([tex]rr[/tex]).

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

[tex]
\[
\begin{array}{|c|c|c|}
\hline
& R & r \\
\hline
R & RR & Rr \\
\hline
r & Rr & rr \\
\hline
\end{array}
\]
[/tex]

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

To determine the expected ratio of red-to-white flowering plants in the phenotypes of the F2 generation, let's examine the genetic cross using a Punnett square.

1. Understand the Parental Genotypes: The two geraniums being crossed in this scenario have Rr genotypes. This means each plant has one allele for red flowers (R) and one allele for white flowers (r).

2. Set Up the Punnett Square: We are crossing two Rr plants, so the possible gametes each can produce are R and r. By filling in the Punnett square, we get the following combinations:

- Top row: R, r
- Side column: R, r

The resulting box (Punnett square) looks like this:

```
| R | r
---------------
R | RR | Rr
r | Rr | rr
```

3. Identify the Genotypes:

- RR: This genotype will result in red flowers.
- Rr: This genotype will also result in red flowers, since the presence of at least one R allele means the trait for red flowers is expressed.
- rr: This genotype will result in white flowers.

4. Count the Genotypes:

- Red-flowering genotypes (RR and Rr): There are 3 instances (RR, Rr, Rr).
- White-flowering genotype (rr): There is 1 instance.

5. Determine the Ratio:

- Red-flowering plants: 3
- White-flowering plants: 1

Thus, the expected ratio of red-to-white flowering plants in the phenotypes of the F2 generation is 3:1.