How do you arrive to the following answers Show work please

How do you arrive to the following answers? Show work please.

Scale color at the tip of the forewing of a butterfly is determined by the alleles at a single locus: A1A1 = red, A1A2 = orange, A1A3 = purple, A2A2 = yellow, A2A3 = green, A3A3 = blue. The frequencies of alleles are: f(A1) = 0.572, f(A2) = 0.286, & f(A3) = 0.142.

3. What is the frequency of heterozygote x heterozygote matings? Answer: 0.32588

4. What proportion of matings could produce 2 but not 1, 3, or 4 genotypes? Answer: 0.48996

Solution

Homozygous: A1A1 = red A2A2 = yellow A3A3 = blue

Heterozygous A1A2 = orange, A1A3 = purple A2A3 = green:

The possibility of having allele A1 in offspring is 0.572 =f1. A2 = 0.286 =f2, f(A3) = 0.142

According to Hardy-Weinberg Law: (f1 +f2 +f3)² = 1

So f₁² +f₂²+f₃²+2f₁f₂+2f₁f₃+2f₂f₃ = 1

So frequency of having heterozygote = 2f1f2+2f1f3+2f2f3; because only these contains the heterozygous group and A1A2A1A3A2A3 can form by only this way

So the frequency of A1A2A1A3A2A3 = 2 x 0.572 x 0.286 + 2 x 0.572 x 0.142 + 2 x 0.286 x 0.142

= 0.327 + 0.162 +0.0812 = 0.570

Now calculate frequency of having cross between two heterozygote = 0.570 x 0.570 =0.325