Questions such as the
Monty Hall problem that ask for a probability
as an answer. The reason the question is difficult is usually because a lack of information makes a unique correct answer impossible. Textbooks usually present a supposedly correct answer anyway, relying on
educational intelligence to provide the missing information.
A trivial example: how likely is it to rain tomorrow? Answer: 50%, either it rains or it doesn't.
Pascal's wager basically relies on the
same argument.