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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]$T_1$[/tex], [tex]$T_2$[/tex], and [tex]$T_3$[/tex].

The numbers of individuals with each of the possible genotypes are shown in the table.
\begin{tabular}{|l|l|}
\hline Genotype & Number of individuals \\
\hline [tex]$T_1 T_1$[/tex] & 50 \\
\hline [tex]$T_1 T_2$[/tex] & 60 \\
\hline [tex]$T_1 T_3$[/tex] & 40 \\
\hline [tex]$T_2 T_2$[/tex] & 50 \\
\hline [tex]$T_2 T_3$[/tex] & 55 \\
\hline [tex]$T_3 T_3$[/tex] & 45 \\
\hline
\end{tabular}

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

A. [tex]$36\%$[/tex]
B. [tex]$72\%$[/tex]
C. [tex]$28\%$[/tex]
D. [tex]$55\%$[/tex]

Sagot :

GinnyAnswer
To determine the frequency of the [tex]\( T2 \)[/tex] allele, let's go through the calculations step by step:

1. Count the total number of individuals:
- For the [tex]\( T1T1 \)[/tex] genotype, there are 50 individuals.
- For the [tex]\( T1T2 \)[/tex] genotype, there are 60 individuals.
- For the [tex]\( T1T3 \)[/tex] genotype, there are 40 individuals.
- For the [tex]\( T2T2 \)[/tex] genotype, there are 50 individuals.
- For the [tex]\( T2T3 \)[/tex] genotype, there are 55 individuals.
- For the [tex]\( T3T3 \)[/tex] genotype, there are 45 individuals.

Adding these up gives us the total number of individuals:
[tex]\[ 50 + 60 + 40 + 50 + 55 + 45 = 300 \][/tex]

2. Count the total number of [tex]\( T2 \)[/tex] alleles:
- Each individual with [tex]\( T2T2 \)[/tex] contributes 2 alleles of [tex]\( T2 \)[/tex]:
[tex]\[ 2 \times 50 = 100 \][/tex]
- Each individual with [tex]\( T1T2 \)[/tex] contributes 1 allele of [tex]\( T2 \)[/tex]:
[tex]\[ 60 \times 1 = 60 \][/tex]
- Each individual with [tex]\( T2T3 \)[/tex] contributes 1 allele of [tex]\( T2 \)[/tex]:
[tex]\[ 55 \times 1 = 55 \][/tex]

Adding these values together gives us the total number of [tex]\( T2 \)[/tex] alleles:
[tex]\[ 100 + 60 + 55 = 215 \][/tex]

3. Calculate the total number of alleles in the population:
Since each individual carries two alleles, the total number of alleles in the population is:
[tex]\[ 2 \times 300 = 600 \][/tex]

4. Calculate the frequency of the [tex]\( T2 \)[/tex] allele:
The frequency of the [tex]\( T2 \)[/tex] allele is given by the ratio of the number of [tex]\( T2 \)[/tex] alleles to the total number of alleles. To find this, we divide the number of [tex]\( T2 \)[/tex] alleles by the total number of alleles:
[tex]\[ \frac{215}{600} \][/tex]

5. Convert the frequency to a percentage:
To convert this frequency to a percentage, we multiply by 100:
[tex]\[ \frac{215}{600} \times 100 \approx 35.83\% \][/tex]

Rounding to the nearest whole number, we get:
[tex]\[ \approx 36\% \][/tex]

Thus, the frequency of the [tex]\( T2 \)[/tex] allele is approximately [tex]\( 36\% \)[/tex].

Therefore, the correct option is:

A. [tex]\( 36\% \)[/tex]
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