To determine the frequency of the \( t \) allele in the population, let's break down the problem step-by-step:
1. Identifying the Total Number of Individuals:
- There are 26 individuals with the \( TT \) genotype.
- There are 64 individuals with the \( Tt \) genotype.
- There are 20 individuals with the \( tt \) genotype.
2. Calculating the Number of Alleles:
Each individual has two alleles. Thus, for the entire population, the total number of alleles is given by:
[tex]\[
2 \times \text{total number of individuals}
\][/tex]
In this case, since total number of individuals = \( 26 + 64 + 20 = 110 \),
[tex]\[
\text{Total number of alleles} = 2 \times 110 = 220
\][/tex]
3. Counting the Alleles:
- Each \( TT \) individual has 2 \( T \) alleles. Therefore, the total number of \( T \) alleles contributed by \( TT \) individuals is:
[tex]\[
2 \times 26 = 52
\][/tex]
- Each \( Tt \) individual has 1 \( T \) allele and 1 \( t \) allele. Therefore, the total number of \( T \) alleles contributed by \( Tt \) individuals is:
[tex]\[
64
\][/tex]
Combining the \( T \) alleles from \( TT \) and \( Tt \) individuals:
[tex]\[
\text{Total number of } T \text{ alleles} = 52 + 64 = 116
\][/tex]
- Each \( t t \) individual has 2 \( t \) alleles. Therefore, the total number of \( t \) alleles contributed by \( t t \) individuals is:
[tex]\[
2 \times 20 = 40
\][/tex]
- Each \( Tt \) individual also contributes 1 \( t \) allele. So, the total number of \( t \) alleles from \( Tt \) individuals is:
[tex]\[
64
\][/tex]
Combining the \( t \) alleles from \( tt \) and \( Tt \) individuals:
[tex]\[
\text{Total number of } t \text{ alleles} = 40 + 64 = 104
\][/tex]
4. Calculating the Frequency of the \( t \) Allele:
The frequency of the \( t \) allele is the number of \( t \) alleles divided by the total number of alleles:
[tex]\[
\text{Frequency of } t = \frac{\text{Total }t \text{ alleles}}{\text{Total number of alleles}} = \frac{104}{220} \approx 0.4727
\][/tex]
Thus, the frequency of the [tex]\( t \)[/tex] allele in the population is approximately [tex]\( 0.47 \)[/tex].
