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]
