Question 8 of 10

A species of fly has two alleles for the length of their legs. The allele for long legs is dominant and is represented by [tex]\( p \)[/tex]. The allele for short legs is recessive and is represented by [tex]\( q \)[/tex]. If 33 of 100 organisms have short legs, what is [tex]\( p \)[/tex]?

Given:
[tex]\[ p^2 + 2pq + q^2 = 1 \][/tex]

A. 0.89
B. 0.43
C. 0.57
D. 0.11



Answer :

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