Guessing the last answer in the test Let's imagine someone passing an exam like shown and filling out the correct answers in tasks 1-11. Then, this someone stops and tries to guess an answer in the last one task (he do not know the right answer). Which answer should he choose?

Since the answers to the tasks were randomly distributed, does it mean that the probability of A12-3 is maximal? Or, since the answers are not dependent on each other, the probability is still 1/4 for any and no matter which line should be chosen?
 A: "Probability" depends highly on the probability distribution.  In this case it's unknown.  We can make assumptions about this unknown distribution, but these are no more than guesses.  Here are three possibilities:


*

*Perhaps (3) is not a valid choice; 1 means "true", 2 means "false", and 4 means "other".  In this case the probability of 3 is zero.

*Perhaps the author of the exam noticed that there haven't been any (3) answers so far, and rearranged the answers to force an answer of 3.  In this case the probability of 3 is one.

*Perhaps the probability is truly equal for all four answers, on every question.  The previous data bears no influence on the answer to the last question in that case.  The probability of 3 is one fourth.
Generally on multiple-choice questions, a student can eliminate one or more of the options as definitely wrong, and choose randomly from the remainder.  If all four answers appear equally plausible, then my advice is to study more instead of trying to look for patterns among the previous answers. :-)
A: Oh, so that's a classical mistake I've almost made, Gambler's fallacy.
