After the amusement comes a still small voice, and therefore, though foolish and weakened by slackness and fatigue, I will attempt an explanation. And what is meant by the verse, “and upon the knees you shall be dandled”? To teach you that there is amusement even in nonsense and absurdity.

To begin with, the question is not defined. We chose some answer — how do we check whether it is correct or not? You can’t check, because the question has no specific content. So there is no question. And consequently there is no answer. So let us go and eat our bread with joy.

But let us suppose the question was: “Which of the following answers yield a consistent result?” That is, each of the answers may be given the title “correct answer” if it merely satisfies the weak condition of consistency. So what is consistency? The answer 0 percent is not consistent, for example. Why? Because the chance of getting the answer 0 percent in a random choice is one quarter. We are looking for an answer that is equal to its own probability of being chosen (a fixed point of the probability function of getting an answer). But there is no such answer. Because there are three possible answers: zero, one quarter, and one half. And the probabilities of getting them are, respectively, one quarter, one half, and one quarter. Therefore, even in this sense, no answer is correct.

And may the Rock of Israel save us from errors and show us wonders from His Torah, to make hinds from scraps, and may our eyes behold the building of the bridal canopy, and may the pain of pregnancy cease, and may seven healthy cows rise from the Nile. Amen, may it be His will.

It should say: the probabilities of getting them are one quarter, one half, one quarter.

You are assuming that the question is: what is the probability that I choose the answer 25%. But it could be interpreted as: what is the probability that I choose answer B. Then B and C are correct. And D is also partially correct (according to your interpretation).

True. And is the claim that the question is not defined at all, and that consistency is not a sufficient condition for “being correct,” itself correct?

In any case, even under that interpretation it comes out that there is no answer: what is the probability that I choose answer B? Then B and C are correct and D is not correct. Therefore the probability of choosing a correct answer is one half. Therefore answer D is correct and answers B and C are not correct. Therefore the probability of choosing a correct answer is one quarter. Therefore B and C are correct and D is not correct. And so on. It follows that there is no consistent answer.

But one could say that if we interpret it as the probability of choosing an index (and not the value), then there is an abundant answer to the question, and one could say that the answer is only B, or say that the answer is only C. It is admittedly not logical that B is an answer and C is not, since their values are identical, but since the answer is defined by the index and we are looking only for consistency, there are two valid possibilities (like an anti-paradox) — either assume that only B is correct, or assume that only C is correct.

What is the probability that from a basket with lots of slips of paper, you take one without looking, and on the slip it will be written the answer to this question?

What is the probability that out of about 4,000 religions (and even more branches), you will be born into a family without choosing which one, and the family will have a religion that knows the correct probability that it is the true religion?