Final answer:
A child will have cystic fibrosis if they inherit two copies of the recessive CFTR gene mutation, one from each carrier parent, which corresponds to a 25% chance if both parents are carriers.
Step-by-step explanation:
The most important factor in determining whether a child will have cystic fibrosis is the genetic makeup of the parents. Specifically, cystic fibrosis is an autosomal recessive disorder, which means that a child must inherit two copies of the faulty gene, one from each parent, to show symptoms of the disease.
If both parents are carriers of the cystic fibrosis transmembrane conductance regulator (CFTR) gene mutation (denoted as Ff in the Punnett square), there is a 25% chance with each pregnancy that the child will receive both recessive alleles (ff) and thus have cystic fibrosis.
The CFTR gene mutation leads to the production of a defective channel protein affecting the transport of Cl- ions in cells, which results in thick and sticky mucus that can damage various organs including the lungs and pancreas. Although there is no cure for cystic fibrosis, advancements in treatment have significantly improved life expectancy and quality of life for patients with CF.