MHB Odds of being correct if choosing a question at random

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Choosing an answer to the question at random presents a paradox regarding the probabilities of correctness. If the answer is 25%, it leads to a contradiction by suggesting a 50% chance of selection. Similarly, assuming the answer is 50% or 60% also results in contradictions. The only consistent outcome arises when considering an answer outside the given options, which yields a 0% chance of being correct. Ultimately, the self-referential nature of the question renders it logically invalid.
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If you choose an answer to this question at random, what is the chance you will be correct.

a. 25%

b.50%

c.60%

d.25%

My answer:
1/3*1/2 + 1/3*1/4 + 1/3*1/4 = 1/6 + 1/6 = 1/3
 
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I have no idea how the given answer is reached.

Suppose the answer is 25%. You will choose that 50% of the time, so the answer is 50%, a contradiction.
Suppose the answer is 50%. You will choose that 25% of the time, so the answer is 25%, a contradiction.
Suppose the answer is 60%. You will choose that 25% of the time, so the answer is 25%, a contradiction.
Suppose the answer is some other value. You will choose that 0% of the time, so the answer is 0%, a consistent result.

But the existence of a consistent result doesn’t make the question "well posed". The self reference makes it logically invalid in the same way that "this statement is false" is invalid.
 
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