Let's first establish a few things.

The #"Hardy-Weinberg equation"# can be seen in two forms:

#color(white)(aaaaaaa)color(magenta)(p^2+2pq+q^2=1)color(white)(aaa)andcolor(white)(aaa)color(orange)(p+q = 1#

**Where:**

#color(magenta)(p^2 = "frequency of homozygous dominant genotype"#

#color(magenta)(2pq = "frequency of heterozygous genotype"#

#color(magenta)(q^2 = "frequency of homozygous recessive genotype"#

**and**

#color(orange)(p = "frequency of dominant allele"#

#color(orange)(q = "frequency of recessive allele"#

#---------------------#

You are told that #16 %# of the population expresses the recessive trait. How can you express a recessive trait? Well, if both alleles of a gene are recessive (homozygous recessive), then the recessive trait is expressed. This is usually indicated with a lowercase letter #("Ex. aa")#

Since we know that #16 %# **of the population expresses the recessive trait** *and* #color(magenta)(q^2)# represents the **frequency of the homozygous recessive genotype**, then we know the following

#color(white)(aaaaaaaaaaaaaaa)color(magenta)(q^2) = 0.16#

Now we want to find the percentage of the population that would be **homozygous for the domnaint trait** so somehow we need to get from

#color(white)(aaaaaaaaaaaaaaa)color(white)(a)color(magenta)(q^2)->color(magenta)(p^2)#

**Steps**

**Take the square root of** #color(magenta)(q^2)#

- #sqrt(color(magenta)(q^2))->sqrt(color(magenta)(0.16))->q=0.4#

**Find p from q**

- #color(orange)(p+q = 1#

- #p = 1-0.4#

- #color(orange)(p) = 0.6#

**Square** #color(orange)(p)# t **o get** #color(magenta)(p^2)#

#p^2->(0.6)^2->0.36#

So, #color(magenta)(p^2) = 0.36# meaning #36%# of the population wouuld be homozygous for the dominant genotype.