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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{30}{100}[/tex]
B. [tex]\frac{84}{100}[/tex]
C. [tex]\frac{10}{300}[/tex]
D. [tex]\frac{134}{200}[/tex]
E. [tex]\frac{100}{200}[/tex]



Answer :

GinnyAnswer
To solve the problem of determining the frequency of the dominant allele in a frog population, follow these steps:

1. Identify the given data:
- Homozygous dominant frogs: 50
- Heterozygous dominant frogs: 34
- Frogs with the recessive trait: 16

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

3. Determine the number of dominant alleles in each group:
- Homozygous dominant frogs have two dominant alleles each. Thus, the total number of dominant alleles from homozygous dominant frogs:
[tex]\[ 50 \times 2 = 100 \][/tex]
- Heterozygous dominant frogs have one dominant allele each. Thus, the total number of dominant alleles from heterozygous dominant frogs:
[tex]\[ 34 \times 1 = 34 \][/tex]

4. Sum the number of dominant alleles:
[tex]\[ \text{Total dominant alleles} = 100 + 34 = 134 \][/tex]

5. Calculate the total number of alleles in the population:
Since each frog contributes two alleles to the gene pool, the total number of alleles is:
[tex]\[ \text{Total alleles} = 100 \times 2 = 200 \][/tex]

6. Calculate the frequency of the dominant allele:
[tex]\[ \text{Frequency of the dominant allele} = \frac{\text{Total dominant alleles}}{\text{Total alleles}} = \frac{134}{200} \][/tex]

7. Compare the calculated frequency with the provided choices:
- A. [tex]\(\frac{30}{100} = 0.30\)[/tex]
- B. [tex]\(\frac{84}{100} = 0.84\)[/tex]
- C. [tex]\(\frac{10}{300} = 0.033\)[/tex]
- D. [tex]\(\frac{134}{200} = 0.67\)[/tex]
- E. [tex]\(\frac{100}{200} = 0.50\)[/tex]

The expression that matches the calculated frequency of the dominant allele [tex]\(\frac{134}{200}\)[/tex] is:
[tex]\[ \boxed{D} \][/tex]

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