To determine the frequency of the [tex]$t$[/tex] allele in this population, we need to follow these steps:
1. Count the total number of alleles:
Given that each plant has 2 alleles, and there are 110 plants in total (26 with genotype [tex]\(TT\)[/tex], 64 with genotype [tex]\(Tt\)[/tex], and 20 with genotype [tex]\(tt\)[/tex]), the total number of alleles is:
[tex]\[
110 \times 2 = 220
\][/tex]
2. Calculate the number of [tex]$t$[/tex] alleles:
- Plants with genotype [tex]\(TT\)[/tex] contribute 0 [tex]\(t\)[/tex] alleles.
- Plants with genotype [tex]\(Tt\)[/tex] each contribute 1 [tex]\(t\)[/tex] allele. Thus, the [tex]\(64\)[/tex] plants of genotype [tex]\(Tt\)[/tex] contribute:
[tex]\[
64 \times 1 = 64 \ t\text{ alleles}
\][/tex]
- Plants with genotype [tex]\(tt\)[/tex] each contribute 2 [tex]\(t\)[/tex] alleles. Thus, the [tex]\(20\)[/tex] plants of genotype [tex]\(tt\)[/tex] contribute:
[tex]\[
20 \times 2 = 40 \ t\text{ alleles}
\][/tex]
Combining these, the total number of [tex]\(t\)[/tex] alleles is:
[tex]\[
0 + 64 + 40 = 104
\][/tex]
3. Determine the frequency of the [tex]$t$[/tex] allele:
The frequency of the [tex]$t$[/tex] allele is the number of [tex]\(t\)[/tex] alleles divided by the total number of alleles:
[tex]\[
\text{Frequency of } t = \frac{\text{Number of } t \text{ alleles}}{\text{Total number of alleles}} = \frac{104}{220}
\][/tex]
Simplifying this fraction, we get:
[tex]\[
\frac{104}{220} \approx 0.4727
\][/tex]
Therefore, the frequency of the [tex]$t$[/tex] allele is approximately [tex]\(0.47\)[/tex]. Thus, the correct answer is:
[tex]\[
\boxed{0.47}
\][/tex]
Hence, the answer is B.
