Carrie has cystic fibrosis which must mean that she has inherited a

The answer to this question would be: recessive gen from his father and recessive gene from his mother.

Cystic fibrosis is a genetic disorder that resulted from the defect at cystic fibrosis transmembrane conductance regulator (CFTR). CFTR has a role in the production of mucus, sweat or the gastric juice. 
The disease is inherited by recessive autosomal gene, which means the patient should get the defective gene from both parents.