Answer :
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.
[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.