To determine the frequency of the [tex]\( T2 \)[/tex] allele, let's go through the calculations step by step:
1. Count the total number of individuals:
- For the [tex]\( T1T1 \)[/tex] genotype, there are 50 individuals.
- For the [tex]\( T1T2 \)[/tex] genotype, there are 60 individuals.
- For the [tex]\( T1T3 \)[/tex] genotype, there are 40 individuals.
- For the [tex]\( T2T2 \)[/tex] genotype, there are 50 individuals.
- For the [tex]\( T2T3 \)[/tex] genotype, there are 55 individuals.
- For the [tex]\( T3T3 \)[/tex] genotype, there are 45 individuals.
Adding these up gives us the total number of individuals:
[tex]\[
50 + 60 + 40 + 50 + 55 + 45 = 300
\][/tex]
2. Count the total number of [tex]\( T2 \)[/tex] alleles:
- Each individual with [tex]\( T2T2 \)[/tex] contributes 2 alleles of [tex]\( T2 \)[/tex]:
[tex]\[ 2 \times 50 = 100 \][/tex]
- Each individual with [tex]\( T1T2 \)[/tex] contributes 1 allele of [tex]\( T2 \)[/tex]:
[tex]\[ 60 \times 1 = 60 \][/tex]
- Each individual with [tex]\( T2T3 \)[/tex] contributes 1 allele of [tex]\( T2 \)[/tex]:
[tex]\[ 55 \times 1 = 55 \][/tex]
Adding these values together gives us the total number of [tex]\( T2 \)[/tex] alleles:
[tex]\[
100 + 60 + 55 = 215
\][/tex]
3. Calculate the total number of alleles in the population:
Since each individual carries two alleles, the total number of alleles in the population is:
[tex]\[
2 \times 300 = 600
\][/tex]
4. Calculate the frequency of the [tex]\( T2 \)[/tex] allele:
The frequency of the [tex]\( T2 \)[/tex] allele is given by the ratio of the number of [tex]\( T2 \)[/tex] alleles to the total number of alleles. To find this, we divide the number of [tex]\( T2 \)[/tex] alleles by the total number of alleles:
[tex]\[
\frac{215}{600}
\][/tex]
5. Convert the frequency to a percentage:
To convert this frequency to a percentage, we multiply by 100:
[tex]\[
\frac{215}{600} \times 100 \approx 35.83\%
\][/tex]
Rounding to the nearest whole number, we get:
[tex]\[
\approx 36\%
\][/tex]
Thus, the frequency of the [tex]\( T2 \)[/tex] allele is approximately [tex]\( 36\% \)[/tex].
Therefore, the correct option is:
A. [tex]\( 36\% \)[/tex]
