Final answer:
Each child of two carriers of cystic fibrosis has a 25% chance of having cystic fibrosis, regardless of the health of previous siblings. Therefore, the probability that the fourth child will have the disorder remains at 25%.
Step-by-step explanation:
If a man and a woman are both carriers of cystic fibrosis, the chance of any child they conceive having the disorder is based on autosomal recessive inheritance patterns. According to a Punnett square analysis, each child has a 25% probability of having cystic fibrosis, a 50% chance of being a carrier, and a 25% chance of not being a carrier or affected. This means that even after having three children without cystic fibrosis, the probability that the couple's fourth child will have the disease remains at 25%.
The mutant CFTR gene responsible for cystic fibrosis is located on chromosome 7 and requires two copies for a child to develop the disease. Carriers of cystic fibrosis, who have only one copy of the mutant gene, can produce enough functional protein to avoid the symptoms but can still pass the gene to their offspring. The fact that the couple has had three unaffected children does not alter the probability for the fourth child, as each child's chances are independent of their siblings'.