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A certain gene in a tree species determines how long it takes for a seed to germinate. In one population, the alleles for this gene are [tex]$T_1, T_2,$[/tex] and [tex]$T_3$[/tex].

The numbers of individuals with each of the possible genotypes are shown in the table below:

\begin{tabular}{|l|l|}
\hline
Genotype & Number of Individuals \\
\hline
[tex]$T_1T_1$[/tex] & 50 \\
\hline
[tex]$T_1T_2$[/tex] & 60 \\
\hline
[tex]$T_1T_3$[/tex] & 40 \\
\hline
[tex]$T_2T_2$[/tex] & 50 \\
\hline
[tex]$T_2T_3$[/tex] & 55 \\
\hline
[tex]$T_3T_3$[/tex] & 45 \\
\hline
\end{tabular}

What is the frequency of the [tex]$T_2$[/tex] allele?

A. [tex]$72\%$[/tex]

B. [tex]$36\%$[/tex]

C. [tex]$28\%$[/tex]

D. [tex]$55\%$[/tex]



Answer :

GinnyAnswer
To determine the frequency of the [tex]\( T2 \)[/tex] allele in the given population, we need to follow these steps:

1. Calculate the Total Number of Individuals:
We first sum up the numbers of individuals for all genotypes.
[tex]\[ \text{Total individuals} = 50 (\text{T1T1}) + 60 (\text{T1T2}) + 40 (\text{T1T3}) + 50 (\text{T2T2}) + 55 (\text{T2T3}) + 45 (\text{T3T3}) = 300 \][/tex]

2. Count the Total Number of [tex]\( T2 \)[/tex] Alleles:
The [tex]\( T2 \)[/tex] alleles come from the genotypes:
- [tex]\( T2T2 \)[/tex]: Each [tex]\( T2T2 \)[/tex] individual contributes 2 [tex]\( T2 \)[/tex] alleles.
- [tex]\( T1T2 \)[/tex] and [tex]\( T2T3 \)[/tex]: Each [tex]\( T1T2 \)[/tex] and [tex]\( T2T3 \)[/tex] individual contributes 1 [tex]\( T2 \)[/tex] allele.

Counting the alleles gives:
[tex]\[ \text{Total } T2 \text{ alleles} = 2 \times \text{(number of T2T2 individuals)} + \text{(number of T1T2 individuals)} + \text{(number of T2T3 individuals)} \][/tex]
Substituting the given numbers:
[tex]\[ \text{Total } T2 \text{ alleles} = 2 \times 50 (\text{T2T2}) + 60 (\text{T1T2}) + 55 (\text{T2T3}) = 100 + 60 + 55 = 215 \][/tex]

3. Calculate the Frequency of the [tex]\( T2 \)[/tex] Allele:
Each individual has 2 alleles. Thus, the total number of alleles in the population is:
[tex]\[ \text{Total alleles} = 2 \times \text{Total individuals} = 2 \times 300 = 600 \][/tex]
The frequency of the [tex]\( T2 \)[/tex] allele is:
[tex]\[ \text{Frequency of } T2 = \frac{\text{Number of } T2 \text{ alleles}}{\text{Total number of alleles}} = \frac{215}{600} \approx 0.3583 \][/tex]

4. Convert the Frequency into a Percentage:
[tex]\[ \text{Percentage of } T2 = 0.3583 \times 100 \approx 35.83\% \][/tex]

Hence, the correct answer is:
B. [tex]\( 36\%\)[/tex] (rounded to the nearest percent).

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