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Hamsters can have a variety of colors, including golden, where the allele for golden color [tex]\((G)\)[/tex] is dominant over the allele for black color [tex]\((g)\)[/tex]. The table shows the genotypes and phenotypes for a small population of hamsters.

[tex]\[
\begin{tabular}{|l|l|l|}
\hline Genotype & Phenotype & \begin{tabular}{l}
Number of \\
hamsters
\end{tabular} \\
\hline
G G & Golden & 15 \\
\hline
G g & Golden & 30 \\
\hline
g g & Black & 5 \\
\hline
\end{tabular}
\][/tex]

What is the frequency of the golden phenotype?

A. [tex]\(\frac{20}{35}\)[/tex]

B. [tex]\(\frac{45}{50}\)[/tex]

C. [tex]\(\frac{15}{35}\)[/tex]

D. [tex]\(\frac{35}{50}\)[/tex]



Answer :

GinnyAnswer
To determine the frequency of the golden phenotype among the hamster population, we should follow these steps:

1. Total Number of Hamsters:
We start by finding the total number of hamsters in the population. This is the sum of all hamsters regardless of their genotype.
- Number of [tex]$GG$[/tex] hamsters: 15
- Number of [tex]$Gg$[/tex] hamsters: 30
- Number of [tex]$gg$[/tex] hamsters: 5

Therefore, the total number of hamsters is:
[tex]\[ 15 + 30 + 5 = 50 \][/tex]

2. Number of Golden Hamsters:
Next, we calculate the total number of golden hamsters. Both [tex]$GG$[/tex] and [tex]$Gg$[/tex] genotypes result in a golden phenotype.
- Number of [tex]$GG$[/tex] hamsters: 15
- Number of [tex]$Gg$[/tex] hamsters: 30

Adding these together gives the total number of golden hamsters:
[tex]\[ 15 + 30 = 45 \][/tex]

3. Frequency of the Golden Phenotype:
The frequency of the golden phenotype is the number of golden hamsters divided by the total number of hamsters.
[tex]\[ \text{Frequency of golden phenotype} = \frac{\text{Number of golden hamsters}}{\text{Total number of hamsters}} = \frac{45}{50} \][/tex]

Thus, the frequency of the golden phenotype is [tex]\( \frac{45}{50} \)[/tex] or simplified, [tex]\( 0.9 \)[/tex]. Therefore, the correct answer is:

B. [tex]\( \frac{45}{50} \)[/tex]

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