Tay-sachs is an autosomal recessive disease. a couple (jack and jill) is worried about having a child who has tay-sachs, because jack had a brother with the deadly disease. since they wanted to have children, they sought the advice of a genetic counselor. during the course of the interview the counselor determined that jack’s parents were not affected with tay-sachs, yet his brother had it. what is immediately known about the genotypes of jack’s parents? is the genotype of jack immediately known? under what circumstances could jack and jill have a child with tay-sachs? assume that neither jack nor jill has tay-sachs.

Jack parents' genotype = Both Heterozygous dominant (carrier)

Jack's genotype = could be homozygous dominant or heterozygous dominant

Jack and Jill can have a child with Tay-Sachs if both of them are heterozygous dominant for the disease.

Explanation:

Since Jack's brother died of the disease, his parents should be heterozygous dominant for the disease. Both the parents served as the carrier (Aa x Aa, assuming that allele "a" is responsible for Tay-Sachs disease) and had one affected child (Jack's bother= "aa").  

Since Jack is not affected by the disease, he could be homozygous dominant (AA) or heterozygous dominant (Aa). But, his exact genotype could not be determined by the given information.

Child of Jack and Jill could be affected with the disease only if both of them are heterozygous dominant (Jack: Aa and Jill: Aa) and serve as the carrier for the disease.