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?

A. 2 red: 2 white
B. All red
C. 1 red: 3 white
D. 3 red: 1 white

Sure! Let's go through the problem step by step to determine the expected ratio of red-to-white flowering plants in the F2 generation of geraniums.

1. Understanding Alleles and Phenotypes:
- The trait for red flowers is controlled by the allele [tex]\( R \)[/tex]. A plant will have red flowers if its genotype is [tex]\( RR \)[/tex] or [tex]\( Rr \)[/tex]. Therefore, both [tex]\( RR \)[/tex] and [tex]\( Rr \)[/tex] result in red flowering plants.
- The trait for white flowers is controlled by the allele [tex]\( r \)[/tex]. A plant will have white flowers only if its genotype is [tex]\( rr \)[/tex].

2. Setting Up the Cross:
- We are given that the horticulturalist crosses two geraniums from the F1 generation, both with genotype [tex]\( Rr \)[/tex]. This means each parent plant can pass on either an [tex]\( R \)[/tex] or an [tex]\( r \)[/tex] allele.

3. Creating the Punnett Square:
- We set up a Punnett square to illustrate all possible combinations of alleles that the offspring can inherit from the parent plants:
```
| R | r |
---------------
R | RR | Rr |
---------------
r | Rr | rr |
```

4. Analyzing the Results:
- There are 4 possible outcomes from this cross: [tex]\( RR \)[/tex], [tex]\( Rr \)[/tex], [tex]\( Rr \)[/tex], and [tex]\( rr \)[/tex].
- [tex]\( RR \)[/tex]: Red flowers
- [tex]\( Rr \)[/tex]: Red flowers
- [tex]\( rr \)[/tex]: White flowers

5. Counting the Phenotypes:
- There are 3 cases that result in red flowering plants ([tex]\( RR \)[/tex] and two [tex]\( Rr \)[/tex]).
- There is 1 case that results in white flowering plants ([tex]\( rr \)[/tex]).

6. Determining the Phenotypic Ratio:
- Based on the counts, the expected ratio of red (combination of [tex]\( RR \)[/tex] and [tex]\( Rr \)[/tex]) to white ([tex]\( rr \)[/tex]) flowering plants is 3 red to 1 white.

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