Let's solve this step-by-step:
1. Given Information:
- There are a total of 100 organisms.
- 20 of these organisms have green eyes.
2. Understanding the Green Allele:
- The green allele is recessive, denoted by [tex]\( q \)[/tex].
- This means organisms with green eyes have two recessive alleles ([tex]\( q^2 \)[/tex]).
- The frequency of organisms with green eyes in the population is therefore the fraction of green-eyed organisms: [tex]\(\frac{20}{100} = 0.2 \)[/tex].
3. Finding the Frequency of the Recessive Allele, [tex]\( q \)[/tex]:
- We have [tex]\[ q^2 = 0.2 \][/tex].
- To find [tex]\( q \)[/tex], take the square root of both sides: [tex]\[ q = \sqrt{0.2} \][/tex].
4. Calculating the Square Root:
- Using the square root operation, we obtain: [tex]\[ q = 0.4472135954999579 \][/tex].
5. Choosing the Closest Answer:
- Among the options provided:
- A. 0.89
- B. 0.55
- C. 0.45
- D. 0.80
- The closest value to the calculated [tex]\( q \)[/tex] (0.4472135954999579) is option C: 0.45.
Thus, the correct answer is C. 0.45.
