To determine the frequency of the T2 allele in the population, we need to follow a systematic approach. Here’s a detailed step-by-step solution:
1. Count the Number of Alleles:
Each individual has 2 alleles for the gene. Therefore, if we know the number of individuals of each genotype, we can calculate the total number of alleles in the population.
[tex]\[
\text{Number of alleles} = \text{Number of individuals} \times 2
\][/tex]
Below is the total number of alleles in the population:
[tex]\[
\text{Total number of individuals} = 50 + 60 + 40 + 50 + 55 + 45 = 300
\][/tex]
So, the total number of alleles in the population is:
[tex]\[
\text{Total number of alleles} = 300 \times 2 = 600
\][/tex]
2. Count the Number of T2 Alleles:
We need to account for all the T2 alleles present in each genotype category:
- [tex]\( T2T2 \)[/tex]: Each individual has 2 T2 alleles.
[tex]\[
50 \text{ (individuals with } T2T2) \times 2 = 100 \text{ T2 alleles}
\][/tex]
- [tex]\( T1T2 \)[/tex] and [tex]\( T2T3 \)[/tex]: Each individual has 1 T2 allele.
[tex]\[
60 \text{ (individuals with } T1T2) + 55 \text{ (individuals with } T2T3) = 115 \text{ T2 alleles}
\][/tex]
Adding these, the total number of T2 alleles in the population is:
[tex]\[
100 + 115 = 215 \text{ T2 alleles}
\][/tex]
3. Calculate the Frequency of the T2 Allele:
To find the frequency of the T2 allele, divide the number of T2 alleles by the total number of alleles and multiply by 100 to convert it to a percentage.
[tex]\[
\text{Frequency of } T2 = \left( \frac{\text{Number of } T2 \text{ alleles}}{\text{Total number of alleles}} \right) \times 100
\][/tex]
[tex]\[
\text{Frequency of } T2 = \left( \frac{215}{600} \right) \times 100 \approx 35.83\%
\][/tex]
Therefore, the closest option to 35.83% is 36%.
Hence, the frequency of the [tex]\( T2 \)[/tex] allele is [tex]\( \boxed{36\%} \)[/tex].
