# Another one of those math questions...

Some guy in my office asked me this question.

If you were to choose randomly, what is the chance that you will answer this question correctly?

A) 25%

B) 50%

C) 60%

D) 25%

I was like “…boooo”.

well assuming that you mean choosing A B C or D , then it depends on what the correct answer is …for example if the correctr answer is 25% then your chance of selelcting it is 2/4 but if the correct answer is B or C then the chance is 1/3…

def no solution. With 4 unique options, you know one solution exists, and picking it is 25%.

You just blew my mind.

im going to use this as a pick up line tonight …i will let you all know how it goes

I believe the answer is B) Why? Because if you choose A) you are indirectly choosing D) with it. So, lets combine them for argument sake. (25% + 25% = 50%) So, if you choose A), you have to choose D), but that is not possible. The only reasonable way to pick either A) or D) is to pick B). So, in reality, you are just picking between B) and C). B), I feel, is the right answer.

But, one could also argue that by picking B), you are picking out of 4 options so it should be 25%. In my opinion, the simplifying assumption that A) and D) cannot be picked together might be the only answer to the paradox.

Assuming that 25% is wrong as its in there twice, you’re left with choice B & C, which gives you a 50% of the correct answer - choice B. However, choice B is a 1/4 answer option, so you’re back to 25%. I would say this is undefined

My guess 50% because if the answer is indeed 25% then I stand a 1 in 2 chance of getting it correct and if the answer is NOT 25% then I still stand a 1 in 2 chance of getting it correct

You’re introducing a bayesian probabilties where there are none. You can’t say if the answer is NOT this one then I have a 1/2 chance of getting it right as a totally random chooser would not have that knowledge. The answer is there is no answer as this question is logically null.

Agreed - the question contains a fallacy of composition. Ergo sum, it logically defeats itself. Tautological really.

Assuming you have to choose from those 4 choices randomly: - 50% chance of picking A or D, both of which say the answer is 25%. Not correct. - 25% chance of picking B, which says the answer is 50%. Not correct. - 25% chance of picking C, which says the answer is 60%. Not correct. So, the answer is 0%. The answer to the question is defined not just by the number of choices but also by what the answer to those choices is.

What have I done…

How about 50% because I will be either right or wrong no matter what I pick. So 50%

It doesn’t seem that tough to me…randomly picking from the 4 choices there is a 25% chance of picking any single choice. If just one of them said 25%, instead of two, the answer would be a clear cut 25%. Two of them say 25% which throws a wrench into that and means the answer is no longer 25%, so the answer is you have zero chance when choosing RANDOMLY. Process of my elimination, useful in exam taking.