To determine the value of [tex]\( q \)[/tex], we need to follow these steps:
1. Understand the given data:
- The Hardy-Weinberg equilibrium equation is [tex]\( p^2 + 2pq + q^2 = 1 \)[/tex].
- We are told that 59 out of 100 organisms have the red allele, which is recessive. Being recessive means that these organisms have the genotype [tex]\( q^2 \)[/tex].
2. Calculate [tex]\( q^2 \)[/tex]:
- Since 59 out of 100 organisms exhibit the recessive phenotype, we have:
[tex]\[
q^2 = \frac{59}{100} = 0.59
\][/tex]
3. Solve for [tex]\( q \)[/tex]:
- To find the value of [tex]\( q \)[/tex], take the square root of [tex]\( q^2 \)[/tex]:
[tex]\[
q = \sqrt{0.59}
\][/tex]
- Taking the square root of 0.59, we get:
[tex]\(
q \approx 0.7681145747868608
\)[/tex]
Thus, the value of [tex]\( q \)[/tex] is approximately 0.77.
Therefore, the correct answer is:
D. 0.77
