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 solve the problem, we first note that the trait for red flowers is dominant (allele [tex]$R$[/tex]) and the trait for white flowers is recessive (allele [tex]$r$[/tex]). Since the geraniums in the F1 generation are heterozygous, both have the genotype [tex]$Rr$[/tex]. When two heterozygotes are crossed, the mating is:

[tex]$$
Rr \times Rr
$$[/tex]

We can determine the genotypes of the offspring using a Punnett square. First, list the gametes each parent can produce:

- The first parent can produce gametes: [tex]$R$[/tex] and [tex]$r$[/tex].
- The second parent can also produce gametes: [tex]$R$[/tex] and [tex]$r$[/tex].

The Punnett square is set up as follows:

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

From the Punnett square:

1. The top-left square is [tex]$RR$[/tex].
2. The top-right square is [tex]$Rr$[/tex].
3. The bottom-left square is [tex]$Rr$[/tex].
4. The bottom-right square is [tex]$rr$[/tex].

Since red is dominant, both [tex]$RR$[/tex] and [tex]$Rr$[/tex] will have red flowers. Only [tex]$rr$[/tex] will have white flowers.

Counting the outcomes:
- Red-flowering plants: [tex]$RR$[/tex] (1 outcome) + [tex]$Rr$[/tex] (2 outcomes) = 3 outcomes.
- White-flowering plants: [tex]$rr$[/tex] = 1 outcome.

Thus, the ratio of red-to-white flowering plants in the F2 generation is:

[tex]$$
3:1.
$$[/tex]

This completes the step-by-step solution.