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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][tex]$TT$[/tex][/tex] & Tall & 28 \\
\hline
[tex]$Tt$[/tex] & Tall & 46 \\
\hline
[tex]$tt$[/tex] & Short & 26 \\
\hline
\end{tabular}

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

Hint: There are a total of 200 alleles for this gene in the population.

A. 0.37
B. 0.28
C. 0.51
D. 0.74



Answer :

GinnyAnswer
To determine the frequency of the [tex]\( T \)[/tex] allele in the population, we need to follow a methodical approach by examining the number of each genotype and then calculating the allele frequencies.

Here are the steps:

1. Identify the Genotype Distribution:
- Number of individuals with genotype [tex]\( TT \)[/tex]: 28
- Number of individuals with genotype [tex]\( Tt \)[/tex]: 46
- Number of individuals with genotype [tex]\( tt \)[/tex]: 26

2. Calculate the Total Number of Alleles:
Each individual has 2 alleles. Therefore, the total number of alleles in the population is given by:
[tex]\[ \text{Total alleles} = 2 \times (\text{Number of } TT \text{ individuals} + \text{Number of } Tt \text{ individuals} + \text{Number of } tt \text{ individuals}) \][/tex]
Substituting the numbers from the problem:
[tex]\[ \text{Total alleles} = 2 \times (28 + 46 + 26) = 2 \times 100 = 200 \][/tex]

3. Count the Total Number of [tex]\( T \)[/tex] Alleles:
- Each individual with genotype [tex]\( TT \)[/tex] contributes 2 [tex]\( T \)[/tex] alleles.
- Each individual with genotype [tex]\( Tt \)[/tex] contributes 1 [tex]\( T \)[/tex] allele.
- Individuals with genotype [tex]\( tt \)[/tex] do not contribute any [tex]\( T \)[/tex] alleles.

Therefore, the number of [tex]\( T \)[/tex] alleles is calculated as:
[tex]\[ \text{Number of } T \text{ alleles} = 2 \times (\text{Number of } TT \text{ individuals}) + 1 \times (\text{Number of } Tt \text{ individuals}) \][/tex]
[tex]\[ \text{Number of } T \text{ alleles} = 2 \times 28 + 46 = 56 + 46 = 102 \][/tex]

4. Calculate the Frequency of the [tex]\( T \)[/tex] Allele:
The frequency of the [tex]\( T \)[/tex] allele is found by dividing the number of [tex]\( T \)[/tex] alleles by the total number of alleles in the population:
[tex]\[ \text{Frequency of } T = \frac{\text{Number of } T \text{ alleles}}{\text{Total number of alleles}} = \frac{102}{200} = 0.51 \][/tex]

Therefore, the frequency of the [tex]\( T \)[/tex] allele in the population is [tex]\( 0.51 \)[/tex].

The correct answer is:
C. 0.51

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