I got a question that comes from the 1990 released test #61 that I'm completley lost on

61. In a population that is in Hardy-Weinberg equilibrium, the frequency of a recessive allele for a certain hereditary trait is 0.20. What percentage of the individuals in the next generation would be expected to show the dominant trait?
a. 8%
b. 16%
c. 32%
d. 64%
e. 96%

The key says E is the answer but I don't see why or how can you please exlain how this is so... I believe that the reason why I can't get this answer is becasue it's asking of the individuals of the next generation in which case I don't seem to know what to do.... thanks!!!

To solve this question, we need to understand the principles of Hardy-Weinberg equilibrium and how it relates to the inheritance of traits.

In Hardy-Weinberg equilibrium, the frequencies of alleles in a population remain constant across generations, assuming certain conditions are met. These conditions include random mating, a large population size, no migration, no mutation, and no natural selection.

In this question, we are given that the frequency of the recessive allele for the trait is 0.20. Let's denote this allele as q. Since there are only two alleles, the dominant allele (p) and the recessive allele (q), the sum of their frequencies must be 1. Therefore, the frequency of the dominant allele (p) would be 1 - 0.20 = 0.80.

To determine the percentage of individuals in the next generation who would show the dominant trait, we need to calculate the genotype frequencies for the dominant trait using the Hardy-Weinberg equation:

p² + 2pq + q² = 1

In this equation, p² represents the frequency of the homozygous dominant genotype (AA), 2pq represents the frequency of the heterozygous genotype (Aa), and q² represents the frequency of the homozygous recessive genotype (aa).

Given that the frequency of the recessive allele (q) is 0.20, we can substitute this value into the equation to solve for p², 2pq, and q².

Let's start with finding p². We know that q² (the frequency of the recessive genotype) is 0.20² = 0.04. Substituting this into the equation:

p² + 2pq + 0.04 = 1

Since p² + 2pq + q² = 1, we can rearrange the equation to solve for 2pq:

2pq = 1 - p² - q² = 1 - 0.04 = 0.96

Using the value of 2pq = 0.96, we can now determine the frequency of individuals who would show the dominant trait, which is represented by p² + 2pq:

p² + 2pq = p² + 0.96

Since p² + 2pq = 1, we can rearrange the equation to solve for p²:

p² = 1 - 2pq = 1 - 0.96 = 0.04

So, the frequency of individuals who would show the dominant trait is 0.04, or 4%.

However, the question asks for the percentage of individuals in the next generation who would show the dominant trait. Given that the frequency of individuals who would show the dominant trait is 4%, the percentage would be 4%. Therefore, the correct answer is 4% which corresponds to option E.