Best Stat Question Ever?

#1
Got this off Twitter (@galka_max) and found it interesting:

If you choose an answer to this question at random, what is the chance you will get it correct?

A) 25%
B) 50%
C) 60%
D) 25%
 

CowboyBear

Super Moderator
#5
I didn't know that was important. Why do you ask?

It is my understanding that there actually isn't an answer to this question so I don't know how to define, "correct."
If an answer is chosen at random, then each option has a 25% chance of being selected. If, then, there is a single option of 25% that is keyed as correct, the question is consistent: There is an answer such that the probability of selecting it randomly is the same as the displayed percentage, and that answer is keyed as correct.

But in the displayed question, A and D are both 25%, which screws things up. If A was keyed as correct, would D be too?
 

Dason

Ambassador to the humans
#6
It doesn't actually specify what probability distribution would be used to choose "at random". One could make a case for almost any answer.