To solve for [tex]\( q \)[/tex] using the Hardy-Weinberg equation, we'll follow a step-by-step approach:
1. Understand the given data and Hardy-Weinberg principle:
- The Hardy-Weinberg equation is [tex]\( p^2 + 2pq + q^2 = 1 \)[/tex], where:
- [tex]\( p \)[/tex] is the frequency of the dominant allele (purple).
- [tex]\( q \)[/tex] is the frequency of the recessive allele (red).
- [tex]\( p^2 \)[/tex] is the frequency of the homozygous dominant genotype.
- [tex]\( 2pq \)[/tex] is the frequency of the heterozygous genotype.
- [tex]\( q^2 \)[/tex] is the frequency of the homozygous recessive genotype.
2. Analyze the given data:
- We are given that 30 out of 100 organisms are red. Since red organisms are homozygous recessive, this corresponds to [tex]\( q^2 \)[/tex].
- Total number of organisms = 100.
- Number of red organisms = 30.
3. Calculate [tex]\( q^2 \)[/tex]:
[tex]\[
q^2 = \frac{\text{Number of red organisms}}{\text{Total number of organisms}} = \frac{30}{100} = 0.3
\][/tex]
4. Calculate [tex]\( q \)[/tex] by taking the square root of [tex]\( q^2 \)[/tex]:
[tex]\[
q = \sqrt{q^2} = \sqrt{0.3} \approx 0.5477225575051661
\][/tex]
5. Verify the value of [tex]\( q \)[/tex] against the provided options:
- A: [tex]\( 0.70 \)[/tex]
- B: [tex]\( 0.49 \)[/tex]
- C: [tex]\( 0.55 \)[/tex]
- D: [tex]\( 0.30 \)[/tex]
Given the calculated value of [tex]\( q \approx 0.5477225575051661 \)[/tex], the closest option is [tex]\( 0.55 \)[/tex], which corresponds to option C.
6. Conclusion:
The value of [tex]\( q \)[/tex] is approximately [tex]\( 0.55 \)[/tex].
Therefore, the correct answer is:
C. 0.55
