Question

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 p. the allele for short legs is recessive, and is represented by q. if 21 of 100 organisms have short legs, what is p?
$p^2 + 2pq + q^2 = 1$

a. 0.79
b. 0.54
c. 0.46
d. 0.21

Explanation:

Step1: Find \( q^2 \)

Short - legged organisms have the genotype corresponding to \( q^2 \) (since short legs are recessive). Given that 21 out of 100 organisms have short legs, so \( q^{2}=\frac{21}{100} = 0.21\).

Step2: Find \( q \)

Take the square root of \( q^{2} \) to find \( q \). \( q=\sqrt{q^{2}}=\sqrt{0.21}\approx0.458\approx0.46 \) (we can also note that from the Hardy - Weinberg equation \( p + q=1 \), so we can first find \( q \) or use the fact that we need to find \( p^{2} \) by first finding \( p \)). Since \( p + q = 1\), then \( p=1 - q \).

Step3: Find \( p \)

We know that \( p + q=1 \), so \( p = 1 - q \). We found that \( q\approx0.46 \), so \( p=1 - 0.46 = 0.54 \)? Wait, no, wait. Wait, the Hardy - Weinberg equation is \( p^{2}+2pq + q^{2}=1 \) and \( p + q = 1 \). Let's do it correctly. We know that \( q^{2}=0.21 \), so \( q=\sqrt{0.21}\approx0.458\). Then \( p = 1 - q=1 - 0.458 = 0.542\). Then \( p^{2}=(0.542)^{2}\approx0.294\)? No, that's wrong. Wait, no, the question is asking for \( p^{2} \)? Wait, no, wait the options: Let's re - evaluate.

Wait, the short - legged individuals are \( q^{2}=0.21 \). Then \( q=\sqrt{0.21}\approx0.458 \). Then \( p = 1 - q=1 - 0.458 = 0.542 \). But \( p^{2}=(0.542)^{2}\approx0.294 \), which is not in the options. Wait, maybe I made a mistake. Wait, no, the question is asking for \( p^{2} \)? Wait, no, let's check the options again. Wait, the options are A. 0.79, B. 0.54, C. 0.46, D. 0.21. Wait, maybe I misread the question. Wait, the question is "what is \( p^{2} \)"? No, wait, maybe the question is "what is \( p \)"? No, the options are 0.79, 0.54, 0.46, 0.21. Wait, let's start over.

The Hardy - Weinberg principle: \( p \) is the frequency of the dominant allele, \( q \) is the frequency of the recessive allele. The frequency of the homozygous recessive genotype (\( q^{2} \)) is equal to the number of homozygous recessive individuals divided by the total number of individuals. So \( q^{2}=\frac{21}{100}=0.21 \). Then \( q=\sqrt{0.21}\approx0.458 \). Then \( p = 1 - q=1 - 0.458 = 0.542\approx0.54 \). Wait, but \( p^{2}=(0.542)^{2}\approx0.29 \), which is not in the options. Wait, no, maybe the question is asking for \( p \) instead of \( p^{2} \)? No, the question says "what is \( p^{2} \)"? Wait, no, maybe the question is "what is \( p \)"? Wait, the options: B is 0.54, which is approximately \( p \). Wait, maybe there is a mistake in my approach. Wait, let's use the fact that \( p^{2}+2pq + q^{2}=1 \) and \( p + q = 1 \). We know that \( q^{2}=0.21 \), so the frequency of dominant homozygotes (\( p^{2} \)) and heterozygotes (\( 2pq \)) is \( 1 - q^{2}=1 - 0.21 = 0.79 \). But that's \( p^{2}+2pq = 0.79 \). But we need to find \( p^{2} \). Wait, no, maybe the question is asking for \( p \), and there is a typo. Wait, if \( p = 1 - q \), and \( q=\sqrt{0.21}\approx0.46 \), then \( p = 1 - 0.46 = 0.54 \), which is option B. Wait, maybe the question was supposed to ask for \( p \) instead of \( p^{2} \). Given the options, the correct answer is B. 0.54.

Wait, let's check again. The number of short - legged individuals is \( q^{2}=21/100 = 0.21 \). Then \( q=\sqrt{0.21}\approx0.458 \). Then \( p = 1 - q\approx1 - 0.458 = 0.542\approx0.54 \), which is option B.

Answer:

B. 0.54