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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 & Number of individuals \\
\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. 0.90

B. 0.82

C. 0.26

D. 0.53



Answer :

GinnyAnswer
Let's break down the problem and solve it step-by-step.

### Step 1: Identify given information
- The provided table gives us the number of individuals for each genotype.
- Homozygous dominant (TT): 26 individuals
- Heterozygous (Tt): 64 individuals
- Homozygous recessive (tt): 20 individuals

- We are given a hint that there are a total of 220 alleles in the population.

### Step 2: Calculate the number of dominant (T) and recessive (t) alleles
- Each TT individual contributes 2 dominant alleles (T).
- Each Tt individual contributes 1 dominant allele (T) and 1 recessive allele (t).
- Each tt individual contributes 2 recessive alleles (t).

From the information given:
- The number of dominant alleles (T):
[tex]\[ (2 \times \text{number of TT individuals}) + (1 \times \text{number of Tt individuals}) \][/tex]
Substituting the numbers:
[tex]\[ (2 \times 26) + (1 \times 64) = 52 + 64 = 116 \][/tex]

- The number of recessive alleles (t):
[tex]\[ (2 \times \text{number of tt individuals}) + (1 \times \text{number of Tt individuals}) \][/tex]
Substituting the numbers:
[tex]\[ (2 \times 20) + (1 \times 64) = 40 + 64 = 104 \][/tex]

### Step 3: Calculate the frequency of the T allele
- The frequency of an allele is given by the number of copies of that allele divided by the total number of alleles.

Given that the total number of alleles is 220, the frequency of the T allele [tex]\((f(T))\)[/tex] is:
[tex]\[ f(T) = \frac{\text{number of T alleles}}{\text{total number of alleles}} = \frac{116}{220} \][/tex]

### Step 4: Simplify the fraction and round the result
[tex]\[ \frac{116}{220} \approx 0.5272727272727272 \][/tex]

### Conclusion
So, the frequency of the [tex]\( T \)[/tex] allele in the population is approximately [tex]\( 0.53 \)[/tex].

The correct answer is:
[tex]\[ \boxed{0.53} \][/tex]

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