Wooly hair is a rare autosomal dominant trait found only in

Wooly hair is a rare autosomal dominant trait found only in people of Scandinavian descent ___/7 which causes a person\'s hair to resemble the wool of a sheep. A man with wooly hair, who has a normal haired mother, moves to an island where no other Scandinavians live. Assume that no other Scandinavians immigrate to this island, a) What is the chance that this man\'s first great-grandchild will have wooly hair? b) If this man has four great grandchildren in total, what is the chance that exactly one will have wooly hair? You have no information about the intermediate generations.

Solution

50%------answer

The wooly haired male is a heterozygote, because he has the trait and his mother did not.

He must have inherited the normal allele from his mother.

Therefore, he has a 50% chance of passing the wooly allele to his offspring; his offspring have a 50% of passing the allele to their offspring; and

these grandchildren have a 50% chance of passing the allele to their offspring (the wooly haired man’s great-grandchildren).

N= four great children

Since this is an ordered sequence of independent events, we use the product rule: 0.5 ´ 0.5 ´ 0.5 = 0.125, or 12.5%.

Since there are no other Scandinavians on the island, there is an 87.5% chance of the offspring being normal (because they could not inherit the wooly hair allele from anyone else). We use the binomial expansion equation to determine the likelihood that one out of eight great-grandchildren will have wooly hair, where

n = 4,

wooly allel -p = 0.125,

normal allele q = 0.875.

(p + q)4 = p4 + 4p3q + 6p2q2 + 4pq3 + q4

4pq =4 * 0.125*0.875^3

() The answer is 0.334, or 33.4%, of the time.