Topic: A strange probabilistic question
 Message: Posted by: ipe (Nov 2, 2018 05:51AM)
If you choose an answer to this question at random, what is the probability that you will be correct?

A) 25%
B) 50%
C) 0%
D) 25%

:bg:
 Message: Posted by: landmark (Nov 3, 2018 01:09PM)
"this question " is ill-defined.
 Message: Posted by: Scott Cram (Nov 3, 2018 06:40PM)
The choices defat each other in a non-transitive cycle (think rock/paper/scissors, where none of the choices are always the best), so none of the answers can be chosen at random with the correct probability.
 Message: Posted by: landmark (Nov 4, 2018 06:04AM)
Imagine this were not a multiple choice question. Rather than asking the probability of answering the question, ask what is the correct answer.

If it is answerable then there is some probability >0 of being correct if answering at random; if not answerable, then the P=0. There is no way to distinguish between the two cases.
 Message: Posted by: ipe (Nov 4, 2018 08:02AM)
[quote]On Nov 3, 2018, landmark wrote:
"this question " is ill-defined. [/quote]

What if the options would be:

A) 25%
B) 50%
C) This question is ill-defined
D) 25%
 Message: Posted by: ipe (Nov 4, 2018 08:04AM)
[quote]On Nov 3, 2018, Scott Cram wrote:
The choices defat each other in a non-transitive cycle (think rock/paper/scissors, where none of the choices are always the best), so none of the answers can be chosen at random with the correct probability. [/quote]

If you cannot choose the correct answer, so 0% is the correct answer; but you can choose "0%" from the multiple options available. :D
 Message: Posted by: landmark (Nov 5, 2018 04:30PM)
Choice C (ill-defined) case is not an answer; it is a statement about the nature of the question.It could just as well be replaced by "I like this question."
 Message: Posted by: ipe (Nov 6, 2018 03:00AM)
Landmark, I agree with you, I was just in the role of puzzle-proposer. :bg: