Let's solve this step-by-step to determine the frequency of the recessive allele in the population.
1. Identify the genotypes and their frequencies:
- Homozygous dominant (RR): 4
- Heterozygous dominant (Rr): 30
- Homozygous recessive (rr): 25
2. Calculate the total number of individuals in the population:
- Total individuals = 4 (RR) + 30 (Rr) + 25 (rr) = 59
3. Determine the total number of alleles in the population:
- Each individual has 2 alleles, so total alleles = 59 * 2 = 118
4. Calculate the number of recessive alleles:
- Each homozygous recessive individual (rr) has 2 recessive alleles (rr), giving us [tex]\( 25 \times 2 = 50 \)[/tex] recessive alleles.
- Each heterozygous dominant individual (Rr) has 1 recessive allele (r), giving us [tex]\( 30 \times 1 = 30 \)[/tex] recessive alleles.
- Total number of recessive alleles = 50 (from rr) + 30 (from Rr) = 80
5. Calculate the frequency of the recessive allele (r):
- Recessive allele frequency = (Number of recessive alleles) / (Total number of alleles)
- Recessive allele frequency = [tex]\( \frac{80}{118} \)[/tex]
We can see that the correct way to express the frequency is:
[tex]\[ \frac{80}{118} \][/tex]
Given the options provided, none of them exactly match this fraction. However, the closest numerator and denominator represented is that in option C.
After reviewing the options carefully, there seems to be a mistake in the question, as none of the given answers are perfectly correct.
In a well-defined question, the correct set of ratios should be included. But since "the harmonic content" was similar to the required steps, the role of reviewing mathematics precisely and reasonably accurate becomes dominant during selection of mathematical answers.
However, the closest correct analytical option is applying exactly detailedly applicable working calculations.
