Im pretty sure that whenever you would have to guess you would do it correctly because decisionmaking without information is based on luck.

 

Well, the use of Felix Felicis in examinations are banned after all, so it would be logical to say that the potion would give the user an unfair advantage over others. Otherwise, why would it get banned in the first place?

Now, the canon doesn't really give details on this matter, so it's more or less up to individual interpretation. What the canon does tell us is that the potion enables the user to "likely be successful in all their endeavors," given that the said endeavors are possible.

My interpretation is this:

The Felix Felicis cannot provide you knowledge that you didn't know beforehand. Such a thing would be impossible, since your mind cannot produce something out of nothing.

But if you have ever had any sort of access to a piece of information prior to taking the test, Felix could help you remember it, since the knowledge did go through your brain. So, if you heard about something in a lecture, or read it in a textbook, or even heard about it in a conversation, Felix could help you remember it if it comes out in the exam (even if you forgot about the information soon after having access to it).

Now, in the case of multiple choice, I believe the Felix Felicis could help you get all of the questions right, even if you didn't have prior knowledge. After all, you COULD get all of the answers right by guessing. Statistically speaking, the chances of doing so would be extremely rare, but it is still possible. And since it is possible, it would be likely that you would be successful in doing since the Felix Felicis is, after all, a luck potion.

On the other hand, if there is an essay that requires you to actually know the information (and you have absolutely no knowledge of it), then not even Felix would be able to help you from screwing up the test.

 

On the other hand, it might let you spin some very convincing BS. Granted, you usually need to know something about the subject to BS your way through an essay. Though it would be pretty rare to take a test where you have absolutely no knowledge of the subject: most folks have at least picked up a few random bits of info on a subject through random happenstance, books/TV/Movies, etc.