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

The horticulturalist plans to cross a geranium that is true-breeding for red flowers with a geranium that is heterozygous for red flowers.

Which Punnett square best describes this cross?

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

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

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

Sure! Let's go through the problem step-by-step to set up and understand the Punnett square for this genetic cross.

### Problem Overview
We have:

- A true-breeding geranium with red flowers: This means its genotype is homozygous dominant, denoted by [tex]$ RR $[/tex].
- A geranium that is heterozygous for red flowers: This means its genotype is [tex]$ Rr $[/tex].

The task is to determine the potential offspring from crossing these two geraniums.

### Setting up the Punnett Square
A Punnett square helps predict genetic outcomes from a cross between two parents. Here's how to set up the square for this problem:

1. Identify Possible Gametes for Each Parent:
- True-breeding red flower ([tex]$ RR $[/tex]) produces gametes with the allele [tex]$ R $[/tex].
- Heterozygous red flower ([tex]$ Rr $[/tex]) produces gametes with the alleles [tex]$ R $[/tex] and [tex]$ r $[/tex].

2. Create the Punnett Square:

On one side of the square, list the gametes from the first parent ([tex]$ RR $[/tex]), and on the other side, list the gametes from the second parent ([tex]$ Rr $[/tex]).

```
| R | r |
__|____|____|
R | RR | Rr |
__|____|____|
R | RR | Rr |
```

### Outcome of the Punnett Square
- The offspring genotypes are represented in the squares:
- Two squares show [tex]$ RR $[/tex], indicating homozygous dominant offspring.
- Two squares show [tex]$ Rr $[/tex], indicating heterozygous offspring.

### Conclusion
The Punnett square shows that each offspring has a:
- 50% chance of being [tex]$ RR $[/tex] (homozygous red)
- 50% chance of being [tex]$ Rr $[/tex] (heterozygous red)

Thus, the second Punnett square option is correct, displaying these possible outcomes: [tex]$ RR, Rr, RR, Rr $[/tex].