intuitively, which option would you pick? 1, 2 or 3 (see image)

[saqwe]

i guess silver, but like the looks of all of them

[1714815442]

1714815442

[1714815442]

1714815442

[teukon]

How does one "answer" this? My head is full of fog It is strongly reminiscent of "This sentence is false. Is that sentence correct?". Basically, if 40% is correct, you have 40% chance. But if 20% is correct, you have 20% chance. But if they are both correct, then there's 60% chance, which gives 0% chance, which gives 20% chance. So 20% wouldn't keep looping around, but 40% wouldn't either, but they can't both be correct. Should we say there is no answer, the question is a liar paradox?
I can't put my finger on what is "wrong" with the question…

If correct is taken to mean (can consistently be correct) then (B), (C), and (E) are possible and (A) is not.  But then what about (D)?  Could it be "meta-consistently-correct" or something?

More seriously, I would simply say that there is no solution to this question (yes, there is a similarity with the liar paradox).  With a slightly different wording (not saying "... the probability ..." which implies uniqueness) there could be two different consistent solutions, 20% and 40%.  The cause of the apparent paradox is the self-reference in the question.

[BTCurious]

I like these kinds of questions more as polls, actually.
In fact, let's continue this here: https://bitcointalk.org/index.php?topic=50355.0

[molecular]

How does one pronounce "casascius" anyway?

^This

To make this question more interesting you might want to make option (C) 0% and/or slightly rephrase the question.  You might also try something a little bit deeper:

If one of the following five answers to this question is chosen at random what is the chance you will be correct?
A) 0%
B) 20%
C) 40%
D) 80%
E) 40%

How does one "answer" this? My head is full of fog It is strongly reminiscent of "This sentence is false. Is that sentence correct?". Basically, if 40% is correct, you have 40% chance. But if 20% is correct, you have 20% chance. But if they are both correct, then there's 60% chance, which gives 0% chance, which gives 20% chance. So 20% wouldn't keep looping around, but 40% wouldn't either, but they can't both be correct. Should we say there is no answer, the question is a liar paradox?
I can't put my finger on what is "wrong" with the question…

The answer is part of the question, that's what's "wrong" with the question.