What are the chances of this happening?

That would depend on the type of question, how many answers there were, how similar it was to other questions etc... there's really not one answer.  We'd have to know more about the question to narrow it down.
Do all the students get the same three problems?

Was the second exam drawn from the *same pool* of 50 questions as the first one? That seems very strange indeed.

It is conceivable that the setters are being a little malicious, picking harder problems on purpose, I guess.

To answer your actual math question: there are (50 \* 49 \* 48) / (3 \* 2 \* 1) ways to draw a three-question exam from a slate of 50 candidate problems. That's 19,600. Now suppose you didn't study problem X. What are the chances of getting that problem, assuming all the problems have an equal chance of being drawn? (If they are being malicious and drawing the hard problems preferentially, this reasoning doesn't work.) There are (49 \* 48 \* 47) / (3 \* 2 \* 1) exams that *don't* contain the poison problem -- that's 18,424. That means that there are 1,176 exams that do have the poison problem, which is exactly 6%. (That's 3/50, which ought to have been obvious in retrospect!)

For this unfortunate lighting to strike twice, the probability is 6% of 6%, or 0.0036 -- a bit less than four tenths of one percent. This isn't low enough to immediately start jumping up and down complaining about witchcraft. Wait for it to happen a third time -- and then wise up and devote more time to the problems that scare you most!

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