Final answer:
The probability that Bob and Kate's first child will have Prader-Willi is 0%. Since the defective gene from Bob will be silenced due to maternal imprinting, and Kate has two normal copies, the child will not have the syndrome.
Step-by-step explanation:
The probability that Bob and Kate's first child will have Prader-Willi syndrome is 0%. Prader-Willi syndrome is typically caused by a loss of function of genes on chromosome 15. This condition is characterized by symptoms such as constant hunger and can lead to severe obesity in childhood. Importantly, the SNPRN gene involved in Prader-Willi syndrome is maternally imprinted, which means that only the copy inherited from the mother is active while the copy from the father is silenced.
In this scenario, because Bob (the father) carries the mutated allele but it will be imprinted (and therefore silenced), and Kate (the mother) has two normal copies, the child cannot inherit the active mutated allele needed to express the condition. The child will inherit an active normal allele from the mother and an inactive mutated allele from the father, resulting in no expression of Prader-Willi syndrome.