Given that the allele for fuzzy peaches is recessive and has a frequency of 0.7. This means that the frequency of the dominant allele (F) will be (1-0.7) = 0.3.
Let's use the Hardy-Weinberg equation to calculate the expected number of fuzzy peaches in a sample of 500:
p^2 + 2pq + q^2 = 1
where
p = frequency of the dominant allele (F) = 0.3
q = frequency of the recessive allele (f) = 0.7
The genotype frequencies can be calculated as follows:
FF = p^2 = (0.3)^2 = 0.09
Ff = 2pq = 2(0.3)(0.7) = 0.42
ff = q^2 = (0.7)^2 = 0.49
The expected frequency of fuzzy peaches (ff) is 0.49. Therefore, the expected number of fuzzy peaches in a sample of 500 would be:
Number of fuzzy peaches = expected frequency of fuzzy peaches x sample size
= 0.49 x 500
= 245
Therefore, you would expect to find 245 fuzzy peaches in a sample of 500.