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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
Let's determine the frequency of the dominant allele step-by-step:

1. Identify the given data:
- Homozygous dominant frogs (BB): 50
- Heterozygous dominant frogs (Bb): 34
- Recessive frogs (bb): 16

2. Calculate the total population:
[tex]\[ \text{Total population} = 50 + 34 + 16 = 100 \][/tex]

3. Determine the total number of alleles:
Each frog has 2 alleles, therefore:
[tex]\[ \text{Total alleles} = 2 \times \text{Total population} = 2 \times 100 = 200 \][/tex]

4. Calculate the number of dominant alleles:
- Homozygous dominant frogs (BB) have 2 dominant alleles each: [tex]\( 2 \times 50 = 100 \)[/tex]
- Heterozygous dominant frogs (Bb) have 1 dominant allele each: [tex]\( 1 \times 34 = 34 \)[/tex]
[tex]\[ \text{Total dominant alleles} = 100 + 34 = 134 \][/tex]

5. 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]\[ \text{Frequency of dominant allele} = \frac{\text{Total dominant alleles}}{\text{Total alleles}} = \frac{134}{200} \][/tex]

Thus, the correct expression to calculate the frequency of the dominant allele is:
[tex]\[ D. \frac{134}{200} \][/tex]