Okay! Let's solve this problem step by step.
First, we are given that the red allele is recessive. If an organism appears red, it means it must have two recessive alleles (i.e., its genotype is [tex]\( q^2 \)[/tex]). We are also given that there are 59 red organisms out of a total of 100 organisms.
To find the value of [tex]\( q \)[/tex], we need to follow these steps:
1. Calculate the proportion of red organisms:
Since 59 out of 100 organisms are red, the proportion of red organisms is:
[tex]\[
q^2 = \frac{59}{100} = 0.59
\][/tex]
2. Calculate [tex]\( q \)[/tex]:
We know that [tex]\( q^2 = 0.59 \)[/tex]. To find [tex]\( q \)[/tex], we need to take the square root of [tex]\( q^2 \)[/tex]:
[tex]\[
q = \sqrt{0.59} \approx 0.7681
\][/tex]
Given the results, the value of [tex]\( q \approx 0.77 \)[/tex].
So, the correct answer is:
D. 0.77
