Question

In one generation, the frequency of the A allele is 70 percent and the frequency of the a allele is 30 percent. What are the chances of an individual in the next generation having the genotype aa if the population is in genetic equilibrium?
49%
42%
30%
9%

Answer 1

The answer is 9%.

To calculate this we will use some formulas of the Hardy-Weinberg principle:
p² + 2pq + q² = 1 and p + q = 1
where:

p - the frequency of the A allele.
q - the frequency of the a allele.

p² - the frequency of dominant homozygote (with AA genotype)

2pq - the frequency of heterozygote (with Aa genotype)

q² - the frequency of recessive homozygote (with aa genotype)

We know:

p = 70% = 70/100 = 0.7

q = 30% = 30/100 = 0.3

We need to calculate the frequency of the genotype aa:

q² = ?

Since we know the frequency of allele q, it is easy to calculate the frequency of the genotype aa:

q² = 0.3² = 0.09 = 0.09 · 100% = 9%