To determine the value of [tex]\( p \)[/tex] in this problem, we need to use the information given and apply the Hardy-Weinberg equilibrium principle.
1. Understanding the Data:
- We are given that 33% of the organisms have short legs. This corresponds to the recessive genotype [tex]\( q^2 \)[/tex].
- Hence, [tex]\( q^2 = 0.33 \)[/tex].
2. Finding [tex]\( q \)[/tex]:
- To find [tex]\( q \)[/tex], we take the square root of [tex]\( q^2 \)[/tex]:
[tex]\[
q = \sqrt{0.33} \approx 0.5745
\][/tex]
3. Finding [tex]\( p \)[/tex]:
- According to the Hardy-Weinberg principle, the sum of the frequency of the dominant allele ([tex]\( p \)[/tex]) and the recessive allele ([tex]\( q \)[/tex]) in the population must equal 1:
[tex]\[
p + q = 1
\][/tex]
- We already have [tex]\( q \)[/tex] from the previous step:
[tex]\[
p = 1 - q = 1 - 0.5745 \approx 0.4255
\][/tex]
Given these calculations, the allele frequency [tex]\( p \)[/tex] for long legs is found to be approximately 0.4255, which closely matches option B (0.43).
Therefore, the correct answer is:
B. 0.43
