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In a species of plant, the allele for tall plants, [tex]$T$[/tex], is dominant over the allele for short plants, [tex]$t$[/tex]. The table shows the distribution of genotypes in a population of plants.

\begin{tabular}{|l|l|l|}
\hline
Genotype & Phenotype & \begin{tabular}{l}
Number of \\
individuals
\end{tabular} \\
\hline
[tex]$TT$[/tex] & Tall & 26 \\
\hline
[tex]$Tt$[/tex] & Tall & 64 \\
\hline
[tex]$tt$[/tex] & Short & 20 \\
\hline
\end{tabular}

What is the frequency of the [tex]$t$[/tex] allele?

Hint: There are a total of 220 alleles for this gene in the population.

A. 0.47



Answer :

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].

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