Answer:
96
Explanation:
In solving Hardy-Weinberg related question, there are two formulas involved:
p + q = 1 ----------------------------- equation (1)
p² + 2pq + q² = 1 ------------------- equation (2)
where;
p is the frequency of the dominant allele.
q is the frequency of the recessive allele.
p² is the frequency of individuals with the homozygous dominant genotype.
2pq is the frequency of individuals with the heterozygous genotype.
q² is the frequency of individuals with the homozygous recessive genotype.
Total population of rats = 200
32 are white (bb) = q²
168 are black (BB) = p²
How many of the black rats are heterozygous (Bb) at the coat-color locus?
Frequency of individual (q²) = [tex]\frac{Individuals}{Total population}[/tex]
Frequency of individual (q²) = [tex]\frac{32}{200}[/tex]
q² = 0.16
To find q from q²; we take the square root of the both sides
√q² = √0.16
q = 0.4
Using the first equation;
p + q = 1
p + 0.4 = 1
p = 1 - 0.4
p = 0.6
To find how many of the black rats are heterozygous (Bb) at the coat-color locus (i.e 2pq) ; we have
= 2 × p × q
= 2 × 0.6 × 0.4
= 0.48
∴ 0.48 × Total population of rats
= 0.48 × 200
= 96
Hence, there are 96 black rats that are heterozygous (Bb) at the coat-color locus
