To determine the frequency of the black phenotype in the hamster population, follow these steps:
1. Identify the total number of hamsters in the population:
- Golden hamsters with genotype [tex]\(GG\)[/tex]: 12
- Golden hamsters with genotype [tex]\(Gg\)[/tex]: 25
- Black hamsters with genotype [tex]\(gg\)[/tex]: 13
Add these numbers together:
[tex]\[
\text{Total number of hamsters} = 12 + 25 + 13 = 50
\][/tex]
2. Determine the number of black hamsters with genotype [tex]\(gg\)[/tex]:
- From the table, we know there are 13 black hamsters.
3. Calculate the frequency of the black phenotype:
- Frequency is given by the ratio of the number of black hamsters to the total number of hamsters.
[tex]\[
\text{Frequency of black phenotype} = \frac{\text{Number of black hamsters}}{\text{Total number of hamsters}} = \frac{13}{50}
\][/tex]
4. Simplify the fraction (if necessary) and convert to decimal form:
- In this case, [tex]\(\frac{13}{50}\)[/tex] is already in its simplest form and converts to [tex]\(0.26\)[/tex].
Thus, the frequency of the black phenotype is [tex]\( \frac{13}{50} \)[/tex], which corresponds to option B.
