To solve this problem, we can use the Hardy-Weinberg equation, which describes the relationship between the frequencies of alleles and genotypes in a population. The equation is:
p^2 + 2pq + q^2 = 1
where p is the frequency of the dominant allele (in this case, the allele for smooth skin), q is the frequency of the recessive allele (in this case, the allele for bumpy skin), p^2 is the frequency of homozygous dominant individuals, 2pq is the frequency of heterozygous individuals, and q^2 is the frequency of homozygous recessive individuals.
We can start by calculating the frequency of the recessive allele:
q^2 = 85 / total number of frogs
q^2 = 85 / (826 + 375 + 85)
q^2 = 0.073
To find the frequency of the dominant allele, we can use the fact that p + q = 1:
p + q = 1
p = 1 - q
p = 1 - 0.073
p = 0.927
So the frequency of the recessive allele is 0.073, and the frequency of the dominant allele is 0.927.