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In a particular species of frogs, black spots are a dominant trait and their absence is a recessive trait. In a population of frogs, 50 are homozygous for the dominant trait, 34 are heterozygous dominant, and 16 show the recessive trait. Which expression is the correct way to calculate the frequency of the dominant allele?

A. [tex]\frac{50}{100}[/tex]
B. [tex]\frac{84}{100}[/tex]
C. [tex]\frac{50}{200}[/tex]
D. [tex]\frac{134}{200}[/tex]
E. [tex]\frac{100}{200}[/tex]


Sagot :

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]