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.
