Question

question 1 of 10
a plant has two alleles for color. the red allele is recessive, and is represented by q. the purple allele is dominant, and is represented by p. if 76 of 100 organisms are red, what is q?
$p^2 + 2pq + q^2 = 1$

a. 0.76
b. 0.87
c. 0.36
d. 0.13

Explanation:

Step1: Identify the genotype for red plants

Red plants are recessive, so their genotype is \( q^2 \). The number of red organisms is 76 out of 100, so the frequency of \( q^2 \) is \( \frac{76}{100} = 0.76 \)? Wait, no—wait, 76 red? Wait, no, wait: wait, the problem says 76 of 100 are red? Wait, no, wait, maybe I misread. Wait, no, the red allele is recessive, so the frequency of red plants (homozygous recessive) is \( q^2 \). Wait, but 76 out of 100? Wait, no, maybe it's 76 purple? Wait, no, the question says "76 of 100 organisms are red". Wait, no, that can't be, because then \( q^2 = 0.76 \), so \( q = \sqrt{0.76} \approx 0.87 \), which is option B. Wait, let's check again.

The Hardy-Weinberg equation is \( p^2 + 2pq + q^2 = 1 \), where \( p \) is the frequency of the dominant allele, \( q \) is the frequency of the recessive allele. The homozygous dominant is \( p^2 \), heterozygous is \( 2pq \), homozygous recessive is \( q^2 \). Since red is recessive, red plants have genotype \( q^2 \). So the frequency of red plants is \( q^2 \). Wait, the problem says "76 of 100 organisms are red", so \( q^2 = \frac{76}{100} = 0.76 \)? Wait, no, that would mean \( q = \sqrt{0.76} \approx 0.87 \), which is option B. Wait, but let's confirm.

Wait, maybe I made a mistake. Wait, 76 red? So \( q^2 = 76/100 = 0.76 \), so \( q = \sqrt{0.76} \approx 0.87 \). So the answer is B.

Step1: Determine the frequency of \( q^2 \)

The number of red organisms is 76 out of 100, so the frequency of the homozygous recessive genotype (\( q^2 \)) is \( \frac{76}{100} = 0.76 \).

Step2: Calculate \( q \)

To find \( q \), take the square root of \( q^2 \): \( q = \sqrt{q^2} = \sqrt{0.76} \approx 0.87 \).

Answer:

B. 0.87