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Viliam_Bur comments on Andrew Gelman on "the rhetorical power of anecdotes" - Less Wrong Discussion
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To stop this generalization from running too far, it depends on situation: what are the probabilities, rewards and risks. But assuming that there is no danger, yes, even doing random things is an opportunity to learn; and we often do better than random.
About the teacher vs student situation, this can be solved by proper incentives. What about giving +1 point for a correct answer, -1 point for incorrect answer, and 0 points for blank? Then rational students will stop making up stuff that has less than 50% probability to be right.