To determine which expression is correct for calculating the frequency of the dominant allele in a population of frogs, we need to follow several steps.
First, let's organize the information given:
- There are 50 frogs that are homozygous dominant (AA).
- There are 34 frogs that are heterozygous dominant (Aa).
- There are 16 frogs that are homozygous recessive (aa).
Step 1: Calculate the Total Number of Frogs
We find the total number of frogs by adding up all the individuals in each category:
[tex]\[ 50 \text{ (homozygous dominant)} + 34 \text{ (heterozygous dominant)} + 16 \text{ (homozygous recessive)} = 100 \text{ frogs} \][/tex]
Step 2: Determine the Total Number of Alleles
Each frog has two alleles for the trait, so the total number of alleles in the population is:
[tex]\[ 100 \text{ frogs} \times 2 \text{ alleles per frog} = 200 \text{ alleles} \][/tex]
Step 3: Calculate the Number of Dominant Alleles
- Homozygous dominant (AA) frogs each have 2 dominant alleles. Thus, these frogs contribute:
[tex]\[ 50 \text{ frogs} \times 2 \text{ dominant alleles per frog} = 100 \text{ dominant alleles} \][/tex]
- Heterozygous dominant (Aa) frogs each have 1 dominant allele. Thus, these frogs contribute:
[tex]\[ 34 \text{ frogs} \times 1 \text{ dominant allele per frog} = 34 \text{ dominant alleles} \][/tex]
Adding these up gives us the total number of dominant alleles:
[tex]\[ 100 \text{ (from AA) } + 34 \text{ (from Aa) } = 134 \text{ dominant alleles} \][/tex]
Step 4: Calculate the Frequency of the Dominant Allele
The frequency of the dominant allele is the number of dominant alleles divided by the total number of alleles:
[tex]\[ \text{Frequency of dominant allele} = \frac{134 \text{ dominant alleles}}{200 \text{ total alleles}} \][/tex]
Step 5: Identify the Correct Expression
According to our calculations, the correct expression for the frequency of the dominant allele is indeed:
[tex]\[ \frac{134}{200} \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{D} \frac{134}{200} \][/tex]
