[Second] Best Statistics Question Ever

Raymond Johnson

[Boogieman]

“So you’ve got a 2/4 chance if the answer is 25% of getting that correct.”

No, because if you have a 2/4 chance (50%), then 25% is no longer the correct answer. If 50% is the correct answer, then you only have a 25% chance to pick that at random, which means that 50% is not the correct answer either.

[Dr. Sivana]

37.5%

Thank you for a short answer. I had gotten a decent approximation the hard way (Monte Carlo method).

I set up a spreadsheet with two columns of pseudo-random numbers from 0-3. If the cell in the second column matched the cell in the first column, OR if both were either a 0 or 3, I added 1, dividing by the total number of entries (in this case 1,000). So with 378 hits out of a thousand, I was close, but you were correct.

[Paradox]

BTW, if I read it the way I think it sounds, then the answer is 33%.

[Paradox]

Ok, here is the reasoning. Lets deconstruct this trick question.

if you choose the answer to this question at random,

So I assume the questioner has set up this question, in which all the possible correct answers are given in the 4 choices below. I think I have that straight so far. If you choose the answer to this question at random.

Ok, so lets choose either A,B,C,D at random. Do it now and stop, because that is what the questions is asking. We have chosen at random. I am assuming that we are picking with our eyes closed, but actually, it doesnt matter how you pick, and you'll see why later.

Presumably, we dont know the answer, just that it is one of the 4 numbers, but, oh wait, two are the same, so there are only THREE possible answers. Therefore, once we have picked one of the four, we either have a 25, 50, or a 60. One of those three is correct, I am assuming. We have one number in hand, what is the chance that we have the right one? Well, obviously, it is 1 in 3, or 33.3333%.

The question does NOT ask you "what are your chances of picking the right answer at random", it asks "what are your chances of, having picked an answer at random, that you are correct". Slight difference leads to totally different result. Thus the correct answer, which also goes for the "slightly more diabolical version". 33.333% what is the chance it will be correct

[Paradox]

or 0, 25, 33, 50, or 100... depending on what assumptions you make.

[Paradox]

Blast you Russell...

[TheOldLady]

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[MontaniSemperLiberi]

This is why I always hated discrete conditional probability problems.

And if I ever see someone with an urn with any number of red and blue balls inside it, I’m going to smash that urn and burn all the balls.

[MontaniSemperLiberi]

Agree.