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Refer to the following information to answer this question:

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. What ratio of red-to-white-flowering plants would you expect to see in the phenotypes of the F2 generation?

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

Answer :

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

1. Genetic Background:
- The trait for red flowers is governed by the allele [tex]\( R \)[/tex].
- If a plant has the genotype [tex]\( RR \)[/tex] or [tex]\( Rr \)[/tex], it will have red flowers.
- The trait for white flowers is governed by the allele [tex]\( r \)[/tex].
- A plant will have white flowers only if it has the genotype [tex]\( rr \)[/tex].

2. Cross of Two F1 Geraniums:
- The horticulturalist is crossing two geraniums both from the F1 generation with genotype [tex]\( Rr \)[/tex].

3. Punnett Square:
- The Punnett Square for this cross looks like this:

| | [tex]\( R \)[/tex] | [tex]\( r \)[/tex] |
|-------|---------|---------|
| R | [tex]\( RR \)[/tex] | [tex]\( Rr \)[/tex] |
| r | [tex]\( Rr \)[/tex] | [tex]\( rr \)[/tex] |

4. Determine the Genotypes:
- From the Punnett Square, we see the following combinations of genotypes:
- [tex]\( RR \)[/tex]: One occurrence
- [tex]\( Rr \)[/tex]: Two occurrences
- [tex]\( rr \)[/tex]: One occurrence

5. Identify the Phenotypes:
- Red flowers:
- Produced by genotypes [tex]\( RR \)[/tex] and [tex]\( Rr \)[/tex].
- We have 1 [tex]\( RR \)[/tex] and 2 [tex]\( Rr \)[/tex] for a total of 3 red flowering plants.
- White flowers:
- Produced by the genotype [tex]\( rr \)[/tex].
- We have 1 [tex]\( rr \)[/tex].

6. Calculate the Expected Ratio:
- The expected ratio of red to white flowering plants is 3:1.

Therefore, for every four plants, we expect 3 to have red flowers and 1 to have white flowers in the F2 generation.

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