Greg posted this question

The answer seemed obvious to me but I may be missing some deeper point. My answer  under the fold.



.25*.5+.25*.25+.25*.25+.25*.5 = .375 = 37.5%

If I had to guess it seems to me that the confusion results from two sources

1) There are percentage signs in the answers

2) The fact that 50% of the answers are “25%” and 25% of the answers are “50%”


However what if the question were reworded:

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

A) 250

B) 500

C) 600

D) 250


Here the answer is clearly 37.5% and the “lesson” is that there being three possible right answers does not make your chance of picking the right answer at random 33%, because one of the potential right answers has two “balls” associated with it.

However, the question does not say that the answer must among the listed options. It only asks what is the probability that you will be correct if  you answer at random. If there were no percentages signs, no one would assume that the question was self-referential.

Why assume it just because there are?

UPDATE: I still think part of the “cuteness” of this problem is that it is not explicitly self-referential but my commenters are right that they do not specify the set to which the “correct” answer belongs. I simply assumed it was {“25%”, “50%”, “60%}