Statistics probability questions

[StoneTemplePython]

It makes perfectly good sense to ask for the posterior probability of a visiting scholar, given that a student answered 3 questions correctly and without making any assumption that the test has 5 questions. Admittedly the problem is more challenging than the "assume 5 questions" version, and may possibly be beyond the ability/knowledge of the OP, but I really do not know what the instructor intended, so having two possible versions cannot hurt...

First of all, if 3 questions are answered correctly the test must contain $N \geq 3$ questions.$$

I think your response is fair and you are definitely right that the wording is open for multiple interpretations. In my book, having an observation is a very big deal and the wording is silent whether or not the student has even received the assignment... all we have to go on is, that the student "is expected to answer 3 questions correctly." It seems to me that clarity is important generally in math and especially so in probability, but this question is not clear.

That said, maybe OP's prof meant to write a good homework question, but was interrupted by a visitor from Switzerland.