Final answer:
The expected genotypic frequencies would be 200 homozygous dominant (RR), 400 heterozygous (Rr), and 200 homozygous recessive (rr). This matches option b in the question.
Step-by-step explanation:
Given that you've counted 600 blue and 200 red flowers, we first need to realize that the red phenotype is due to being homozygous recessive (rr) since blue is dominant. The Hardy-Weinberg principle provides a way to calculate the expected genotype frequencies if the population is in equilibrium and is not evolving.
Since the blue phenotype can be due to homozygous dominant (RR) or heterozygous (Rr) genotypes, we cannot directly observe the frequencies of these alleles. Nonetheless, we can make some calculations. Let's represent the frequency of the dominant allele (R) as p and that of the recessive allele (r) as q. The frequency of homozygous recessive (rr) is q^2 which we know is 200/800, as there are 200 red flowers out of a total of 800 flowers. Therefore, q must be the square root of 200/800, which is 0.5. Since p + q = 1, then p must also be 0.5. We can now calculate the expected genotypes based on these allele frequencies. The frequency of homozygous dominant (RR) would be p^2 = 0.25, and of heterozygous (Rr) would be 2pq = 0.5.
So, back to our total population of 800 flowers, we would then expect the following:
- Homozygous dominant (blue flowers, RR): p^2 x 800 = 0.25 x 800 = 200
- Heterozygous (blue flowers, Rr): 2pq x 800 = 0.5 x 800 = 400
- Homozygous recessive (red flowers, rr): q^2 x 800 = 0.25 x 800 = 200
This matches with option b, suggesting a genetic structure of 200 RR, 400 Rr, and 200 rr.