Two cousins marry and their first child has a rare autosomal

Two cousins marry and their first child has a rare autosomal recessive trait conferring high musical ability. If they plan to have 6 children, compute the expected chance that exactly four of the six children will inherit this trait. Show all work.

Solution

The the two cousins are unaffected carriers, assume that the gene coding for dominant phenotype is A and the gene coding for recessive phenotype is, a.

Aa* Aa ---> AA(1/4), Aa (1/2), aa (1/4)

Means, 3/4th proportion of offspring will inherit the recessive allele, while 1/4th of the population are homozygous dominant.

The probability of inheriting the recessive allele by 6 of the 4 children is = = [6!(3/4)^4 (1/4)^2] /4!2! = 15 (81/256) (1/16) = 0.2966.