(No) Pasaran I

The problem as I received it:

A professor announces on the first day of class that he doesn’t believe in grades, but the deanery insists; therefore he guarantees every student equal chances of receiving A or B, the grades to be assigned at random. Anyone who is unhappy with this should not take the course for credit.

Doomsday—and the professor gets out his little black grade book. He is about to flip a coin for each student, giving A for heads and B for tails, when he thinks: I didn’t merely promise that each student had the same expectation as every other; I promised an equal chance of A or B. What if this coin—or any coin—is not absolutely fair? What to do?

See P. II for answers.


  1. Anonymous3:43 AM

    It doesn't matter what the distribution of grades is, the coin doesn't have to be fair; the only requirement in such a case is that the probabilities are the same for each flip.

  2. Sorry, Anonymous, but no: the requirement is not merely that each student has the same expectation as every other, but, more strongly, that each student has an equal chance of A or B.

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