Final answer:
The probability that their child will have ADPKD is 50%, assuming the woman inherited the mutation from her heterozygous father and considering the man has two normal PKD1 alleles.
Step-by-step explanation:
The question pertains to the genetic inheritance of autosomal dominant polycystic kidney disease (ADPKD), specifically related to a mutation in the PKD1 gene. Since the woman's father is heterozygous for the PKD1 mutation, the woman has a 50% chance of having inherited the ADPKD-causing mutation. The mother is unaffected, which implies she has two normal alleles for the PKD1 gene. Given that the man has no family history of ADPKD, he most likely has two normal PKD1 alleles.
Therefore, if the woman is a carrier (heterozygous) for the ADPKD-causing mutation, there is a 50% chance that the child will inherit the ADPKD allele from her. If the woman did not inherit the mutation, the chance would be 0%. However, since we aren't provided with information on the woman's genotype, only her father's, we cannot determine her exact carrier status. Assuming she is heterozygous, the probability that their child will have ADPKD is 50%.