MHB Odds of being correct if choosing a question at random

[alexmahone]

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:

Spoiler

1/3*1/2 + 1/3*1/4 + 1/3*1/4 = 1/6 + 1/6 = 1/3

 

[haruspex]

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.