Let's go through the information given step by step and how to calculate the frequency of the dominant allele in the population.
1. Total Number of Frogs:
- Homosexual dominant: 50 frogs.
- Heterozygous dominant: 34 frogs.
- Recessive trait: 16 frogs.
- Therefore, the total number of frogs is [tex]\(50 + 34 + 16 = 100\)[/tex] frogs.
2. Total Number of Alleles:
Since each frog has two alleles, the total number of alleles in the population is [tex]\(2 \times 100 = 200\)[/tex] alleles.
3. Number of Dominant Alleles:
- Homozygous dominant frogs contribute 2 dominant alleles each: [tex]\(50 \times 2 = 100\)[/tex] dominant alleles.
- Heterozygous dominant frogs contribute 1 dominant allele each: [tex]\(34 \times 1 = 34\)[/tex] dominant alleles.
- Frogs with the recessive trait contribute 0 dominant alleles: [tex]\(16 \times 0 = 0\)[/tex] dominant alleles.
- Thus, the total number of dominant alleles in the population is [tex]\(100 + 34 + 0 = 134\)[/tex].
4. Frequency of the Dominant Allele:
To calculate the frequency of the dominant allele, we use the formula:
[tex]\[
\text{Frequency of the dominant allele} = \frac{\text{Total number of dominant alleles}}{\text{Total number of alleles}}
\][/tex]
Using the numbers we calculated:
[tex]\[
\text{Frequency of the dominant allele} = \frac{134}{200} = 0.67
\][/tex]
Given these calculations, the correct way to express this calculation from the given options is:
E. [tex]\(\frac{100}{200}\)[/tex]
