A population of Hawaiian Drosophila is segregating two alleles, P¹ and P², of the phosphoglucose isomerase (PGI) gene. In a sample of 100 flies from this population, 30 were P¹P¹ homozygotes, 60 were P¹P² heterozygotes, and 10 were P²P² homozygotes. 

(a) What are the frequencies of the P¹ and P² alleles in this sample? 

(b) Perform a chi-square test to determine if the genotypes in the sample are in Hardy–Weinberg proportions. 

(c) Assuming that the sample is representative of the population, how many generations of random mating would be required to establish Hardy–Weinberg proportions in the population?