Final answer:
Both parents must be carriers of the autosomal recessive allele that causes cystic fibrosis for their child to have the condition. They each have one copy of the mutated gene and one normal copy, which results in a 25% chance of their child having CF.
Step-by-step explanation:
Cystic fibrosis (CF) is caused by an autosomal recessive allele. If a child has CF, and neither of his parents has the disease, it can be concluded that both parents are carriers for CF. This means that each parent has one copy of the mutated gene (CFTR gene) and one normal copy; therefore, they do not show symptoms of CF themselves.
A child must inherit two copies of the recessive allele, one from each parent, to exhibit the symptoms of CF. According to a Punnett square, two carrier parents (Ff) have a 25% chance of having a child with CF (ff), a 50% chance of having a child who is a carrier (Ff), and a 25% chance of having a child with normal alleles (FF).