Let's analyze the problem step-by-step:
1. Determine the total population of frogs:
- Homozygous dominant (having two dominant alleles): 50
- Heterozygous dominant (having one dominant and one recessive allele): 34
- Recessive trait (having two recessive alleles): 16
The total population is calculated by adding up the three groups:
[tex]\[
50 + 34 + 16 = 100
\][/tex]
2. Calculate the total number of dominant alleles:
- Homozygous dominant frogs each have 2 dominant alleles. Therefore, the total number of dominant alleles from homozygous dominant frogs is:
[tex]\[
50 \times 2 = 100
\][/tex]
- Heterozygous dominant frogs each have 1 dominant allele. Therefore, the total number of dominant alleles from heterozygous dominant frogs is:
[tex]\[
34 \times 1 = 34
\][/tex]
Adding these together, the total number of dominant alleles is:
[tex]\[
100 + 34 = 134
\][/tex]
3. Calculate the total number of alleles in the population:
Each frog has 2 alleles. Therefore, the total number of alleles in the population is:
[tex]\[
100 \times 2 = 200
\][/tex]
4. Calculate the frequency of the dominant allele:
The frequency of the dominant allele is given by dividing the number of dominant alleles by the total number of alleles:
[tex]\[
\text{Frequency of dominant allele} = \frac{134}{200} = 0.67
\][/tex]
So, the correct expression to calculate the frequency of the dominant allele is:
[tex]\[
\frac{134}{200}
\][/tex]
This is not directly one of the choices listed, but it can be inferred that none of the provided expressions are correct in this context.
``` Given the listed options, it seems the choices do not match the correct formula for the frequency of the dominant allele. Hence, there might be a mistake in the options provided or an error in transcription.
