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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 100 frogs, 50 show the dominant trait, 34 are heterozygous dominant, and 16 show the recessive trait. Which expression represents the correct 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 the proportion of dominant alleles in a population of frogs, let's break down the problem step-by-step.

### Step 1: Determine numbers of each frog genotype
Given:
1. Frogs with the dominant homozygous genotype (AA) = 50
2. Frogs with the heterozygous genotype (Aa) = 34
3. Frogs with the recessive homozygous genotype (aa) = 16

### Step 2: Calculate the total number of frogs
To find the total number of frogs:
[tex]\[ \text{Total number of frogs} = 50 + 34 + 16 = 100 \][/tex]

### Step 3: Calculate the number of dominant and recessive alleles
Each homozygous dominant frog (AA) contributes two dominant alleles (A):
[tex]\[ \text{Dominant alleles from AA} = 2 \times 50 = 100 \][/tex]

Each heterozygous frog (Aa) contributes one dominant allele (A) and one recessive allele (a):
[tex]\[ \text{Dominant alleles from Aa} = 34 \][/tex]
[tex]\[ \text{Recessive alleles from Aa} = 34 \][/tex]

Each homozygous recessive frog (aa) only contributes recessive alleles:
[tex]\[ \text{Recessive alleles from aa} = 2 \times 16 = 32 \][/tex]

### Step 4: Total dominant and recessive alleles
Summing the dominant and recessive alleles:
[tex]\[ \text{Total dominant alleles} = 100 + 34 = 134 \][/tex]
[tex]\[ \text{Total recessive alleles} = 34 + 32 = 66 \][/tex]

### Step 5: Calculate the total number of alleles
[tex]\[ \text{Total number of alleles} = 134 + 66 = 200 \][/tex]

### Step 6: Determine the proportion of dominant alleles
The proportion of dominant alleles is:
[tex]\[ \text{Proportion of dominant alleles} = \frac{134}{200} = 0.67 \][/tex]

### Step 7: Identify the matching expression
The provided options are:
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]

The correct matching expression for the proportion of dominant alleles is:
[tex]\[ \frac{134}{200} \][/tex]

Therefore, the correct answer is:

D. [tex]\(\frac{134}{200}\)[/tex]
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