Answer :
To determine the frequency of the recessive allele [tex]\( q \)[/tex] when 30 out of 100 organisms are red, let's follow these steps:
1. Understand the problem: We know that 30 out of 100 organisms are red. Since red is the recessive trait, these organisms must have two copies of the recessive allele, making them homozygous recessive ([tex]\( q^2 \)[/tex]).
2. Calculate the frequency of homozygous recessive organisms: We need to determine the proportion of red organisms within the population. This proportion is given by [tex]\( q^2 \)[/tex].
[tex]\[ q^2 = \frac{\text{number of red organisms}}{\text{total number of organisms}} = \frac{30}{100} = 0.30 \][/tex]
3. Find [tex]\( q \)[/tex]: [tex]\( q \)[/tex] is the square root of [tex]\( q^2 \)[/tex]:
[tex]\[ q = \sqrt{q^2} = \sqrt{0.30} = 0.5477225575051661 \][/tex]
4. Compare with the provided options: From the calculated [tex]\( q \)[/tex], we approximate to the given choices:
A. 0.70
B. 0.49
C. 0.55
D. 0.30
The closest value to our calculated [tex]\( q \)[/tex] (0.5477225575051661) is:
[tex]\[ \boxed{0.55} \][/tex]
Thus, the correct answer is C. 0.55.
1. Understand the problem: We know that 30 out of 100 organisms are red. Since red is the recessive trait, these organisms must have two copies of the recessive allele, making them homozygous recessive ([tex]\( q^2 \)[/tex]).
2. Calculate the frequency of homozygous recessive organisms: We need to determine the proportion of red organisms within the population. This proportion is given by [tex]\( q^2 \)[/tex].
[tex]\[ q^2 = \frac{\text{number of red organisms}}{\text{total number of organisms}} = \frac{30}{100} = 0.30 \][/tex]
3. Find [tex]\( q \)[/tex]: [tex]\( q \)[/tex] is the square root of [tex]\( q^2 \)[/tex]:
[tex]\[ q = \sqrt{q^2} = \sqrt{0.30} = 0.5477225575051661 \][/tex]
4. Compare with the provided options: From the calculated [tex]\( q \)[/tex], we approximate to the given choices:
A. 0.70
B. 0.49
C. 0.55
D. 0.30
The closest value to our calculated [tex]\( q \)[/tex] (0.5477225575051661) is:
[tex]\[ \boxed{0.55} \][/tex]
Thus, the correct answer is C. 0.55.
