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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]



Answer :

GinnyAnswer
To determine the frequency of the dominant allele in a population of frogs, we need to analyze the contributions of each type of frog to the total pool of alleles. Let's break this down step by step.

1. Identify the Total Number of Frogs:
- Homozygous dominant: 50 frogs
- Heterozygous dominant: 34 frogs
- Recessive: 16 frogs

Total number of frogs [tex]\( = 50 + 34 + 16 = 100 \)[/tex]

2. Calculate the Total Number of Alleles:
Each frog has two alleles. Therefore, the total number of alleles is:
[tex]\[ \text{Total alleles} = 2 \times \text{Total number of frogs} = 2 \times 100 = 200 \][/tex]

3. Determine the Number of Dominant Alleles:
- Homozygous dominant frogs (each contributes 2 dominant alleles):
[tex]\[ 50 \text{ homozygous dominant frogs} \times 2 = 100 \text{ dominant alleles} \][/tex]
- Heterozygous dominant frogs (each contributes 1 dominant allele):
[tex]\[ 34 \text{ heterozygous dominant frogs} \times 1 = 34 \text{ dominant alleles} \][/tex]

The total number of dominant alleles:
[tex]\[ \text{Total dominant alleles} = 100 \text{ (from homozygous)} + 34 \text{ (from heterozygous)} = 134 \][/tex]

4. Calculate the Frequency of the Dominant Allele:
The frequency of the dominant allele [tex]\( f(A) \)[/tex] is the number of dominant alleles divided by the total number of alleles:
[tex]\[ f(A) = \frac{\text{Total dominant alleles}}{\text{Total alleles}} = \frac{134}{200} \][/tex]

Given these detailed steps, the correct expression to calculate the frequency of the dominant allele is:

[tex]\[ \boxed{\frac{134}{200}} \][/tex]

Thus, the correct answer is:
D. [tex]$\frac{134}{200}$[/tex]

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