Find the probability if a couple to have 3 children that will be unaffected by Tay-Sachs disease

Question

what is the probability that if the couple has three children, none of them will be affected by the syndrome. refer to the attached picture and show solution.

is it 107/144? can you verify my answer. please refer to the picture below.

The pedigree below shows inheritance of Tay-Sachs disease, an autosomal recessive trait, in two unrelated families. The indicated couple (II1.2 and II.3) would like to have children.

Answer 1

They both have two parents who have the recessive trait. Each of them does not have the disease. Thus, there is a 2/3 chance that each of them has one recessive gene. Thus, there is a 2/3 * 2/3 = 4/9 chance that each of them has the recessive gene. Then, the probability, given that each has the recessive gene, that none of their three children has the disease is (3/4)^3 = 27/64

Then, the probability that none of the children has the disease is

(1 - 4/9) + 4/9*27/64 = 5/9 + 3/16 = (80+27)/144

Your answer is correct.