Consider a population where gene A come in two form, A1 and A2. This gene is not

under selection and random mating occurs with respect to that gene and p= 0.5 and q=
0.5. What are the expected genotype frequencies in the next generation? To do this, you
should find the probabilities of all matings and what the expected outcomes are.

So, p and q are .5, respectively, which I believe are the observed valus. so p^2 and q^2=.0025
so i tried using the H.W equation, but I still come up with .25+.25=.5, but the answer is supposed to be .707, or 70.7% of the population.
Help. Please. you guys are all awesome by the way.

To calculate the expected genotype frequencies in the next generation, we need to consider the probabilities of all possible matings and their outcomes.

In this case, we have two alleles, A1 and A2, with observed frequencies of p = 0.5 and q = 0.5, respectively. Since the gene is not under selection and random mating occurs, we can assume that the population is in Hardy-Weinberg equilibrium.

The Hardy-Weinberg equation states that in a population in equilibrium, the genotype frequencies can be calculated as follows:

- Genotype frequency of A1A1 (p^2)
- Genotype frequency of A1A2 (2pq)
- Genotype frequency of A2A2 (q^2)

So, let's calculate these probabilities using the given values:

1. Genotype frequency of A1A1 (p^2):
p^2 = 0.5^2 = 0.25

2. Genotype frequency of A1A2 (2pq):
2pq = 2 * 0.5 * 0.5 = 0.5

3. Genotype frequency of A2A2 (q^2):
q^2 = 0.5^2 = 0.25

Now, let's add up the genotype frequencies to get the expected genotype frequencies in the next generation:

A1A1 + A1A2 + A2A2 = 0.25 + 0.5 + 0.25 = 1

Therefore, the expected genotype frequencies are:
- A1A1: 0.25 (25%)
- A1A2: 0.5 (50%)
- A2A2: 0.25 (25%)

It seems that the expected genotype frequencies do not match the given answer of 0.707 (70.7%). It is possible that there might be some additional information or calculations involved that are not mentioned in the question. Please double-check the question and any additional information provided to see if there are any other details that need to be considered.