Biology genetics

Question

The autosomal dominant gene determines gout. The penetrance of gout is 20% in male and 0% in female. What is the probability that heterozygous parents will have an affected child?

Answer 1

If an autosomal dominant allele determines gout, then both heterozygotes and dominant homozygotes are affected, except, in this case, females are not affected (i.e. there is 0% penetrance in females, so the trait is sex-limited to males), and only 20% of males with one or two dominant alleles are affected. If two heterozygotes have children, there is a 3/4 chance that each child will inherit a dominant allele from either or both parents. There is an independent 1/2 probability that a child will be male. Independent probabilities are multiplied, so there is 1/2 of 3/4, or 3/8 chance of having a male with at least one dominant allele. For a male with one or two dominant alleles, there is a 20%, or 1/5 probability that he will develop gout. In other words, 1/5 of male children with at least one dominant allele for the gene will develop gout. So, the probability that heterozygous parents have a child who develops gout is 3/8 × 1/5 = 3/40.