The correct answer is C. This patient has polycystic kidney disease (PKD), which leads to the formation of multiple cysts in the kidneys and progressive decrements in renal function, eventually resulting in renal failure (evidenced by the increased BUN and creatinine). PKD is most commonly caused by a genetic defect in the PKD1 gene and is inherited in an autosomal dominant fashion. It is most likely that this patient is heterozygous for the mutation, thus, the chance that a child inherited the mutated gene is 0.5, or 50%. The figure below is a Punnett square that demonstrates the risk of mating an affected individual (Aa) with a homozygous unaffected individual (aa). The affected offspring (Aa) are shaded.

<0.01 (choice A) or less than 1% could not occur in an autosomal dominant disease with one carrier. The risk would be at least 50%.
0.25 (choice B) or 25% could be the risk of getting a disease with autosomal recessive inheritance when both parents are carriers (see figure below).
The affected genotype (aa) is shaded.

0.67 (choice D) or 67%, could be the risk of a phenotypically normal person being a carrier of an autosomal recessive disease when both parents are carriers (see figure above).
While 1.0 or 100% (choice E) would be correct if the father was homozygous for the genetic mutation, based on his family history, it is more likely that he is heterozygous.
This is a multi-step question.
What is the question asking?
The question is asking you to determine the likelihood that the patient's offspring will inherit the disease described in the vignette, assuming that the mother is not also a carrier.
What is the first step?
The first step is to make a diagnosis. You should note the early onset of cystic kidney disease (the patient is 40 years old) and the fact that the man?s father died at age 49 of the same disease. The patient was also told that his disease is hereditary and that his kidney function would continue to decline. These findings strongly suggest that he has polycystic kidney disease (PKD), caused by a mutation in the PKD1 gene.
What is the next step?
Knowing that the man has PKD, you should recall that the disease is transmitted in an autosomal dominant fashion, meaning there is a 1 in 2 (0.5: choice C) chance that the patient would pass the disorder on to his children.
One mnemonic to help remember autosomal dominant diseases is Very Powerful DOMINANT Humans:
Von Willebrand disease / Von Hippel-Lindau
Pseudo-hypoparathyroidism
Dystrophia myotonica
Osteogenesis imperfecta / Osler-Weber-Rendu
Marfan syndrome
Intermittent porphyria
Neurofibromatosis
Adult polycystic kidney disease / Achondroplasia
Noonan syndrome
Tuberous sclerosis
Hypercholesterolemia / Huntingdon disease / Hypertrophic obstructive cardiomyopathy / Hereditary spherocytosis / Hereditary nonpolyposis coli / Hereditary hemorrhagic telangiectasia
Can other answers be eliminated?
Once you've established that the probability of an individual with an autosomal dominant disease passing it to their children is 0.5, all other answer choices (choices A, B, D, and E) can be eliminated.
What is the single best answer and why?
0.50 (choice C) is the single best answer because it is the probability that a child will inherit an autosomal dominant allele from a parent who is expressing the disease.
MedEssentials (4th Ed.): pp. 327
First Aid (2019): pp. 592.2
First Aid (2018): pp. 588.1
First Aid (2017): pp. 573.1
Pathoma (2018-2019): pp. 125.4
Pathoma (2014-2017): pp. 125.4