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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]$T T$[/tex] & Tall & 28 \\
\hline [tex]$T t$[/tex] & Tall & 46 \\
\hline [tex]$t t$[/tex] & Short & 26 \\
\hline
\end{tabular}

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

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

A. 0.28

B. 0.37

C. 0.74

D. 0.51

Sagot :

GinnyAnswer
To determine the frequency of the [tex]\( T \)[/tex] allele in the population, we need to follow these steps:

1. Identify the frequency of each genotype:

- Tall homozygous ([tex]\( TT \)[/tex]): 28 individuals
- Tall heterozygous ([tex]\( Tt \)[/tex]): 46 individuals
- Short homozygous ([tex]\( tt \)[/tex]): 26 individuals

2. Calculate the total number of individuals in the population:

[tex]\[ \text{Total number of individuals} = 28 + 46 + 26 = 100 \][/tex]

3. Determine the total number of alleles in the population:

Each individual has 2 alleles so:

[tex]\[ \text{Total number of alleles} = 100 \times 2 = 200 \][/tex]

4. Calculate the total number of [tex]\( T \)[/tex] alleles:

- Each [tex]\( TT \)[/tex] individual contributes 2 [tex]\( T \)[/tex] alleles. Since there are 28 [tex]\( TT \)[/tex] individuals:

[tex]\[ \text{Number of } T \text{ alleles from } TT \text{ individuals} = 28 \times 2 = 56 \][/tex]

- Each [tex]\( Tt \)[/tex] individual contributes 1 [tex]\( T \)[/tex] allele. Since there are 46 [tex]\( Tt \)[/tex] individuals:

[tex]\[ \text{Number of } T \text{ alleles from } Tt \text{ individuals} = 46 \times 1 = 46 \][/tex]

- [tex]\( tt \)[/tex] individuals contribute 0 [tex]\( T \)[/tex] alleles.

5. Sum the total number of [tex]\( T \)[/tex] alleles:

[tex]\[ \text{Total number of } T \text{ alleles} = 56 + 46 = 102 \][/tex]

6. Calculate the frequency of the [tex]\( T \)[/tex] allele:

The frequency of an allele is the number of that allele in the population divided by the total number of alleles.

[tex]\[ \text{Frequency of } T \text{ allele} = \frac{\text{Number of } T \text{ alleles}}{\text{Total number of alleles}} = \frac{102}{200} = 0.51 \][/tex]

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

The correct answer is:

D. [tex]\( 0.51 \)[/tex]
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