To solve the problem of determining the frequency of the dominant allele in a frog population, follow these steps:
1. Identify the given data:
- Homozygous dominant frogs: 50
- Heterozygous dominant frogs: 34
- Frogs with the recessive trait: 16
2. Calculate the total population of frogs:
[tex]\[
\text{Total population} = 50 + 34 + 16 = 100
\][/tex]
3. Determine the number of dominant alleles in each group:
- Homozygous dominant frogs have two dominant alleles each. Thus, the total number of dominant alleles from homozygous dominant frogs:
[tex]\[
50 \times 2 = 100
\][/tex]
- Heterozygous dominant frogs have one dominant allele each. Thus, the total number of dominant alleles from heterozygous dominant frogs:
[tex]\[
34 \times 1 = 34
\][/tex]
4. Sum the number of dominant alleles:
[tex]\[
\text{Total dominant alleles} = 100 + 34 = 134
\][/tex]
5. Calculate the total number of alleles in the population:
Since each frog contributes two alleles to the gene pool, the total number of alleles is:
[tex]\[
\text{Total alleles} = 100 \times 2 = 200
\][/tex]
6. Calculate the frequency of the dominant allele:
[tex]\[
\text{Frequency of the dominant allele} = \frac{\text{Total dominant alleles}}{\text{Total alleles}} = \frac{134}{200}
\][/tex]
7. Compare the calculated frequency with the provided choices:
- A. [tex]\(\frac{30}{100} = 0.30\)[/tex]
- B. [tex]\(\frac{84}{100} = 0.84\)[/tex]
- C. [tex]\(\frac{10}{300} = 0.033\)[/tex]
- D. [tex]\(\frac{134}{200} = 0.67\)[/tex]
- E. [tex]\(\frac{100}{200} = 0.50\)[/tex]
The expression that matches the calculated frequency of the dominant allele [tex]\(\frac{134}{200}\)[/tex] is:
[tex]\[
\boxed{D}
\][/tex]
