To determine the frequency of the golden phenotype among the hamsters, let's follow these steps:
1. Identify the number of hamsters with each genotype:
- Hamsters with genotype [tex]\( GG \)[/tex]: 15
- Hamsters with genotype [tex]\( Gg \)[/tex]: 30
- Hamsters with genotype [tex]\( gg \)[/tex]: 5
2. Calculate the total number of hamsters:
[tex]\[
\text{Total number of hamsters} = 15 + 30 + 5 = 50
\][/tex]
3. Determine the total number of golden hamsters:
- Both [tex]\( GG \)[/tex] and [tex]\( Gg \)[/tex] genotypes will result in a golden phenotype since [tex]\( G \)[/tex] is dominant over [tex]\( g \)[/tex].
[tex]\[
\text{Golden hamsters} = 15 + 30 = 45
\][/tex]
4. Calculate the frequency of the golden phenotype:
[tex]\[
\text{Frequency of golden phenotype} = \frac{\text{Number of golden hamsters}}{\text{Total number of hamsters}} = \frac{45}{50}
\][/tex]
5. Convert the fraction to a decimal for clarity:
[tex]\[
\frac{45}{50} = 0.9
\][/tex]
Therefore, the frequency of the golden phenotype is [tex]\(\frac{45}{50}\)[/tex].
Thus, the correct answer is:
A. [tex]\( \frac{45}{50} \)[/tex]
