Question
Question 7 There are 100 students in a class. Ninety-six did well in the course whereas four blew it totally and received a grade of F. Sorry. In the highly unlikely event that these traits are genetic rather than environmental, if these traits involve dominant and recessive alleles, and if the four (4%) represent the frequency of the homozygous recessive condition, please calculate the frequency of heterozygous individuals (2pq). a 16% b 29% c 32% d 57%
Answers
GPT-4o mini
To solve the problem, we need to apply the Hardy-Weinberg principle, which is used to calculate the frequencies of genotypes in a population that is not evolving.
Given that 4% of the students (4 out of 100) represent the homozygous recessive individuals (ff, with genotype frequency \( q^2 = 0.04 \)), we can find \( q \) (the frequency of the recessive allele).
1. **Calculate \( q \):**
\[
q = \sqrt{q^2} = \sqrt{0.04} = 0.2
\]
2. **Calculate \( p \):**
Since \( p + q = 1 \):
\[
p = 1 - q = 1 - 0.2 = 0.8
\]
3. **Calculate the frequency of heterozygous individuals (2pq):**
\[
2pq = 2 \cdot p \cdot q = 2 \cdot 0.8 \cdot 0.2 = 0.32
\]
Since the frequency of heterozygous individuals (2pq) is 0.32, we can convert it to a percentage:
\[
0.32 \times 100 = 32\%
\]
Thus, the frequency of heterozygous individuals is **32%**.
The answer is **c) 32%**.
Given that 4% of the students (4 out of 100) represent the homozygous recessive individuals (ff, with genotype frequency \( q^2 = 0.04 \)), we can find \( q \) (the frequency of the recessive allele).
1. **Calculate \( q \):**
\[
q = \sqrt{q^2} = \sqrt{0.04} = 0.2
\]
2. **Calculate \( p \):**
Since \( p + q = 1 \):
\[
p = 1 - q = 1 - 0.2 = 0.8
\]
3. **Calculate the frequency of heterozygous individuals (2pq):**
\[
2pq = 2 \cdot p \cdot q = 2 \cdot 0.8 \cdot 0.2 = 0.32
\]
Since the frequency of heterozygous individuals (2pq) is 0.32, we can convert it to a percentage:
\[
0.32 \times 100 = 32\%
\]
Thus, the frequency of heterozygous individuals is **32%**.
The answer is **c) 32%**.