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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 :

GinnyAnswer
To determine the correct expression for calculating the frequency of the dominant allele in a population of frogs, let's go through the problem step-by-step.

### Step 1: Understanding the Population
In this population:
- There are 50 frogs that are homozygous for the dominant trait (black spots). Each homozygous dominant frog (BB) contributes 2 dominant alleles (B).
- There are 34 frogs that are heterozygous dominant (Bb). Each heterozygous frog contributes 1 dominant allele (B) and 1 recessive allele (b).
- There are 16 frogs that show the recessive trait (bb). Each homozygous recessive frog contributes 2 recessive alleles (b).

### Step 2: Calculating the Total Number of Frogs
The total number of frogs in the population is:
[tex]\[ 50 \text{ (dominant homozygous)} + 34 \text{ (heterozygous dominant)} + 16 \text{ (recessive)} = 100 \text{ frogs} \][/tex]

### Step 3: Counting the Total Number of Alleles
Since each frog has 2 alleles (one from each parent):
[tex]\[ \text{Total number of alleles} = 100 \text{ frogs} \times 2 \text{ alleles per frog} = 200 \text{ alleles} \][/tex]

### Step 4: Counting the Number of Dominant Alleles
Now, let's count the number of dominant alleles (B) in the population:
- The 50 homozygous dominant frogs (BB) contribute [tex]\( 50 \times 2 = 100 \)[/tex] dominant alleles.
- The 34 heterozygous dominant frogs (Bb) contribute [tex]\( 34 \times 1 = 34 \)[/tex] dominant alleles.

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

### Step 5: Calculating the Frequency of the Dominant Allele
The frequency of the dominant allele (B) is the number of dominant alleles divided by the total number of alleles:
[tex]\[ \text{Frequency of dominant allele} = \frac{\text{Number of dominant alleles}}{\text{Total number of alleles}} = \frac{134}{200} \][/tex]

### Final Step: Selecting the Correct Answer
From the above calculation, the correct expression representing the frequency of the dominant allele is:
[tex]\[ \boxed{\frac{134}{200}} \][/tex]

This matches option D. Therefore, option D is the correct answer:
D. [tex]\(\frac{134}{200}\)[/tex]
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