To determine the frequency of the [tex]\( T \)[/tex] allele in the population, we need to follow these steps:
1. Identify the frequency of each genotype:
- Tall homozygous ([tex]\( TT \)[/tex]): 28 individuals
- Tall heterozygous ([tex]\( Tt \)[/tex]): 46 individuals
- Short homozygous ([tex]\( tt \)[/tex]): 26 individuals
2. Calculate the total number of individuals in the population:
[tex]\[
\text{Total number of individuals} = 28 + 46 + 26 = 100
\][/tex]
3. Determine the total number of alleles in the population:
Each individual has 2 alleles so:
[tex]\[
\text{Total number of alleles} = 100 \times 2 = 200
\][/tex]
4. Calculate the total number of [tex]\( T \)[/tex] alleles:
- Each [tex]\( TT \)[/tex] individual contributes 2 [tex]\( T \)[/tex] alleles. Since there are 28 [tex]\( TT \)[/tex] individuals:
[tex]\[
\text{Number of } T \text{ alleles from } TT \text{ individuals} = 28 \times 2 = 56
\][/tex]
- Each [tex]\( Tt \)[/tex] individual contributes 1 [tex]\( T \)[/tex] allele. Since there are 46 [tex]\( Tt \)[/tex] individuals:
[tex]\[
\text{Number of } T \text{ alleles from } Tt \text{ individuals} = 46 \times 1 = 46
\][/tex]
- [tex]\( tt \)[/tex] individuals contribute 0 [tex]\( T \)[/tex] alleles.
5. Sum the total number of [tex]\( T \)[/tex] alleles:
[tex]\[
\text{Total number of } T \text{ alleles} = 56 + 46 = 102
\][/tex]
6. Calculate the frequency of the [tex]\( T \)[/tex] allele:
The frequency of an allele is the number of that allele in the population divided by the total number of alleles.
[tex]\[
\text{Frequency of } T \text{ allele} = \frac{\text{Number of } T \text{ alleles}}{\text{Total number of alleles}} = \frac{102}{200} = 0.51
\][/tex]
Therefore, the frequency of the [tex]\( T \)[/tex] allele in this population is [tex]\( 0.51 \)[/tex].
The correct answer is:
D. [tex]\( 0.51 \)[/tex]
