Let's solve this problem step by step to determine the frequency of the golden phenotype in the hamster population.
1. Identify the Number of Hamsters for Each Genotype:
- The number of hamsters with genotype [tex]\( GG \)[/tex] (golden) is 15.
- The number of hamsters with genotype [tex]\( Gg \)[/tex] (golden) is 30.
- The number of hamsters with genotype [tex]\( gg \)[/tex] (black) is 5.
2. Calculate the Total Number of Hamsters:
To find the total number of hamsters in the population, we simply sum up all the hamsters:
[tex]\[
\text{Total hamsters} = 15 (GG) + 30 (Gg) + 5 (gg) = 50
\][/tex]
3. Determine the Number of Golden Hamsters:
The number of golden hamsters includes those with genotype [tex]\( GG \)[/tex] and [tex]\( Gg \)[/tex]:
[tex]\[
\text{Golden hamsters} = 15 (GG) + 30 (Gg) = 45
\][/tex]
4. Calculate the Frequency of the Golden Phenotype:
The frequency of the golden phenotype is calculated by dividing the number of golden hamsters 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]\[
\frac{45}{50} = 0.9
\][/tex]
The correct answer is:
D. [tex]\(\frac{45}{50}\)[/tex]
