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].

The Punnett square below demonstrates the cross of two geraniums from the F1 generation:

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

We begin by recognizing that the red-flower trait is dominant. This means that a plant with genotype [tex]$RR$[/tex] or [tex]$Rr$[/tex] will have red flowers, while only the homozygous recessive genotype [tex]$rr$[/tex] will result in white flowers.

Consider a cross between two heterozygous plants (each with genotype [tex]$Rr$[/tex]). To find the frequencies of the genotypes in the offspring, we set up a Punnett square:

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

From the Punnett square, we see the following probabilities:
- Genotype [tex]$RR$[/tex]: [tex]$\frac{1}{4}$[/tex]
- Genotype [tex]$Rr$[/tex]: [tex]$\frac{2}{4}$[/tex]
- Genotype [tex]$rr$[/tex]: [tex]$\frac{1}{4}$[/tex]

Since both [tex]$RR$[/tex] and [tex]$Rr$[/tex] result in red flowers, the overall probability for red flowers is:

[tex]$$
\text{Probability of red} = \frac{1}{4} + \frac{2}{4} = \frac{3}{4}
$$[/tex]

The probability for white flowers (only [tex]$rr$[/tex]) is:

[tex]$$
\text{Probability of white} = \frac{1}{4}
$$[/tex]

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

[tex]$$
\frac{3/4}{1/4} = 3:1.
$$[/tex]

Therefore, the horticulturalist should expect to see 3 red-flowering plants for every 1 white-flowering plant in the F2 generation.