MHB Odds of being correct if choosing a question at random

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The discussion centers on the logical paradox of determining the probability of selecting the correct answer to a self-referential question. The options presented are 25%, 50%, 60%, and 25%. Analyzing each option reveals contradictions, leading to the conclusion that the question is inherently flawed. The only consistent outcome is that if the answer is any value other than those provided, the probability is 0%, highlighting the logical invalidity of self-referential questions.

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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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