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Cystic fibrosis is an autosomal recessive disorder caused by the presence of two deleterious alleles for the cystic fibrosis transmembrane conductance regulator (CFTR) protein. This genetic disorder affects the patient’s lungs, pancreas, kidneys, liver and intestine and the main complaint is the inability to breathe well.

A ‘healthy woman’ whose maternal aunt had the disease is trying to determine the probability that she and her husband could have their first and only three children, all unaffected by cystic fibrosis. Her father does not come from a high-risk population. Her husband’s brother and sister died of the disease as teenagers.

What is the probability that the couple’s first three children will not be affected with cystic fibrosis?


$\left(\cfrac{1}{2}\times \cfrac{2}{3}\times \cfrac{2}{3}\times \cfrac{1}{4}\right)^2= 0.003086=3.086\times{10}^{-3}$


$\left(\cfrac{1}{2}\times \cfrac{2}{3}\times \cfrac{3}{4}\right)^3= 0.003906=3.906\times{10}^{-3}$


$\left(\cfrac{2}{3}\times \cfrac{1}{3}\times \cfrac{1}{4}\right)^3= 0.000009526=9.5268\times{10}^{-6}$


$\left(\cfrac{2}{3}\times \cfrac{1}{3}\times \cfrac{3}{4}\right)^3= 0.00463=4.6\times{10}^{-3}$

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