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Sagot :
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]
### 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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