The most accurate explanation for a child being born with cystic fibrosis when no one in the family has the disorder or is known to carry the gene would be:
b. There was a mutation in the DNA, either in one of the gametes or the fertilized egg.
Cystic fibrosis is caused by mutations in the CFTR gene, and if neither parent shows symptoms or has a family history of the disorder, it is possible that one or both parents could be carriers (asymptomatic) or that a new mutation occurred in the child’s DNA. This is a relatively rare scenario, but it is a valid explanation for the appearance of an inherited recessive disorder.