Question

Consider an autosomal recessive neurological disorder that is lethal in childhood. in a population in hardy-weinberg equilibrium, 1 in 750 infants are affected with this condition.
a. what is the frequency of the dominant allele in this population?
b. assuming mating occurs at random in this population, what is the probability that a couple are both carriers of this disorder?

Answer 1

a. what is the frequency of the dominant allele in this population?
Let say N is dominant allele and n is the recessive allele. The disease is autosomal recessive so the patient should be homozygous recessive(nn).
If the frequency of nn is 1/750, then the frequency of n would be: √(1/750)= 0.0365 = 3.65%


b. assuming mating occurs at random in this population, what is the probability that a couple are both carriers of this disorder?
If the frequency of n is 3.65%, the frequency of N would be:
1=n+N
1=3.65%+N
N= 96.35%

The frequency of carrier(Nn) in population would be:
Nn= 2*N*n
Nn= 2 * 3.65% * 96.35%
Nn= 0.0703
The chance that both of the parent is carrier would be: 0.07*0.07= 0.0049= 0.49%