"Try not to think too hard."
October 28, 2011 11:56 AM Subscribe

Found on a classroom chalkboard: The best statistics question ever.

Opinions within the post, and in a separate Google+ conversation, are divided on whether the problem is solvable at all.

(Once you've solved this one, you can head over here for more super-challenging math problems. Hey, who knows, you might turn out to be this kid!

posted by jbickers (264 comments total) 75 users marked this as a favorite

Easy; the airplane never takes off.
posted by Mayor West at 11:57 AM on October 28, 2011 [26 favorites]

I have no goddamn idea, but I know I'm going to enjoy reading this thread.
posted by box at 11:58 AM on October 28, 2011 [6 favorites]

That was an awesome sequence of

"Pfft! This!"

"Wait -- that?"

"But then --"

and then head-explodey stuff.
posted by Shepherd at 12:00 PM on October 28, 2011 [18 favorites]

I think it is B. So, by that logic it must be anything except B.
posted by soelo at 12:00 PM on October 28, 2011 [2 favorites]

"Ha ha ha ... oh ... ow."
posted by griphus at 12:00 PM on October 28, 2011 [2 favorites]

Oh god.
posted by pemberkins at 12:01 PM on October 28, 2011 [1 favorite]

Guys, I just looked into this a little bit and I have to give credit where credit is due: my cat's breath does in fact smell like cat food.
posted by cortex at 12:01 PM on October 28, 2011 [48 favorites]

If all multiple-choice tests were Kafkaesque liar's-paradox nightmares like this, the world would be a lot more entertaining. (Which is to say thanks for the reminder: I haven't thought of Infocom's Bureaucracy in a while.)
posted by RogerB at 12:01 PM on October 28, 2011 [4 favorites]

Schrodinger's cat's breath, however, smells like poison.

Sometimes.
posted by maryr at 12:02 PM on October 28, 2011 [11 favorites]

According to the Kaplan method you should choose A and move on.

Hi, I'm saturday_morning and LSAT prep is killing my soul.
posted by saturday_morning at 12:03 PM on October 28, 2011 [18 favorites]

The difficulty arises because there might be one, two or zero correct responses among the four choices. You have to know which is the correct answer before you can ascertain the correct answer. It's insoluble.
posted by unSane at 12:04 PM on October 28, 2011 [7 favorites]

Damnit chalkboard stop making my brain hurt. I dropped out of college so I never had to see you again and now you followed me to the Internet.
posted by Ad hominem at 12:05 PM on October 28, 2011 [6 favorites]

The answer is 0%. It is not a multiple choice question.
posted by Plutor at 12:05 PM on October 28, 2011 [14 favorites]

The premise as-stated is flawed: since the problem was found on an office chalkboard and not a classroom chalkboard, the answer is clearly (C)...
posted by muddgirl at 12:06 PM on October 28, 2011 [1 favorite]

The question is under-specified, for one thing. Is the question answered correctly when the correct value is selected or only when the correct letter is selected? In other words, if the answer were 25%, are (A) and (D) both correct or would only one of them be?

If it's the latter then the answer is pretty clearly whichever of (A) and (D) is the acceptable answer. I think that's the only non-paradoxical solution.
posted by jedicus at 12:06 PM on October 28, 2011 [5 favorites]

B
posted by the_very_hungry_caterpillar at 12:06 PM on October 28, 2011

It's obviously B, is there some trick I'm missing?
posted by bhnyc at 12:06 PM on October 28, 2011

I've been too busy trying to confirm whether this is the best statistics question ever or the best probability question ever to have gotten around to actually attempting to solve the problem itself. Hazy memories of high school math + pedantic tendencies = excellent Google-based procrastination.
posted by EvaDestruction at 12:07 PM on October 28, 2011

hint: the correct answer to the question may not be the correct answer to this question
posted by 2bucksplus at 12:07 PM on October 28, 2011 [2 favorites]

E) none of the above.
posted by Homeboy Trouble at 12:08 PM on October 28, 2011 [4 favorites]

I'm just tickled by the thought that those replies are from the real Paulo Ferreira
posted by fullerine at 12:08 PM on October 28, 2011

It would be even better if C was "0%" instead of "60%".
posted by dirtdirt at 12:08 PM on October 28, 2011 [9 favorites]

The only winning move is...
posted by gurple at 12:08 PM on October 28, 2011 [2 favorites]

If the correct answer is B, there is a 25% chance of choosing it, so the correct answer is A or D, which means there is a 50% chance of choosing it, which means the correct answer is A or D, and so on...
posted by unSane at 12:08 PM on October 28, 2011 [13 favorites]

I'm waiting for XKCD to weigh in on this.
posted by drezdn at 12:10 PM on October 28, 2011 [5 favorites]

I think it would be more fun with:

a) 25%
b) 50%
c) 50%
d) 100%

But maybe I'm missing some humor value in "60%"?
posted by gurple at 12:11 PM on October 28, 2011

I'm not sure I get it. Is this any more mind bending than: "This sentence is false. Is the previous sentence true or false?"
posted by justkevin at 12:11 PM on October 28, 2011

It's obviously B, is there some trick I'm missing?

If the answer is B than you actually only have a 25% chance of picking the right answer, which means the answer is both A and D, which means you actually only have a 25% chance of picking the right answer, which means the answer is both A and D, which means you actually only have a 25% chance of picking the right answer, which means the answer is both A and D, which means you actually only have a 25% chance of picking the right answer, which means the answer is both A and D, which means you actually only have a 25% chance of picking the right answer, which means the answer is both A and D,which means you actually only have a 25% chance of picking the right answer...
posted by Panjandrum at 12:11 PM on October 28, 2011 [8 favorites]

Is this any more mind bending than: "This sentence is false. Is the previous sentence true or false?"

There are four answers instead of two.
posted by mrgrimm at 12:12 PM on October 28, 2011 [3 favorites]

It really is not recursive. B.
posted by yesster at 12:12 PM on October 28, 2011 [1 favorite]

Mods please delete this post before somebody gets hurt
posted by villanelles at dawn at 12:12 PM on October 28, 2011 [6 favorites]

We can just all walk away and pretend we never saw it
posted by villanelles at dawn at 12:13 PM on October 28, 2011 [6 favorites]

You have no reason to believe this sentence.
posted by P.o.B. at 12:13 PM on October 28, 2011 [1 favorite]

I freaking hate math.
posted by govtdrone at 12:13 PM on October 28, 2011 [1 favorite]

Oops, cut and paste fail. I apologize and shall henceforth write all my answers up on a typewriter and submit them to Mathowie for editing and approval.
posted by Panjandrum at 12:13 PM on October 28, 2011 [1 favorite]

If you like crazy multiple choice tests try this
posted by get off of my cloud at 12:14 PM on October 28, 2011 [12 favorites]

It would be even better if C was "0%" instead of "60%"

Or 75%.

I however have found the correct answer. The question asks "how often will you be right," and I'm calibrated to be correct sixty per cent of the time. So it's C, obviously.
posted by zippy at 12:14 PM on October 28, 2011

I'm not sure I get it. Is this any more mind bending than: "This sentence is false. Is the previous sentence true or false?"

Nope.
posted by DLWM at 12:14 PM on October 28, 2011

So many nascent internet AI's are just breaking down weeping right now.
posted by The Whelk at 12:14 PM on October 28, 2011 [2 favorites]

I got 12%

WTF?
posted by mazola at 12:15 PM on October 28, 2011

Once you answer this, go take the Self-Referential Aptitude Test (click on the title), for more head-asplodey goodness.
posted by jocelmeow at 12:16 PM on October 28, 2011 [14 favorites]

And on top of it all, I just lost The Game. And now so did you!
posted by The Deej at 12:18 PM on October 28, 2011 [9 favorites]

You can apply case analysis:

Case 1: the answer is 25%. Therefore the answer is 50%. Inconsistent.
Case 2: the answer is 50%. Therefore the answer is 25%. Inconsistent.
Case 3: the answer is 60%. Therefore the answer is 25%. Inconsistent.

There is no consistent answer among the choices, so the answer is 'none of the above'.
posted by unSane at 12:19 PM on October 28, 2011 [28 favorites]

I have devised a simple but correct proof, however, the comment box is too small to contain it.
posted by Pogo_Fuzzybutt at 12:19 PM on October 28, 2011 [39 favorites]

Also, please show your work. On this postage stamp.
posted by jiawen at 12:20 PM on October 28, 2011 [1 favorite]

According to my pocket zen calculator, the correct answer is "A suffusion of yellow."
posted by Graygorey at 12:20 PM on October 28, 2011 [14 favorites]

It really is not recursive. B.

"It really is not recursive" is an improper assumption. The question asks what the odds are of being able to randomly pick the correct answer. Nothing says to ignore the content of the answers themselves.
posted by Sticherbeast at 12:20 PM on October 28, 2011

You can place 25% of your answer here and we'll extrapolate the remaining 60% ourselves.
posted by CancerMan at 12:21 PM on October 28, 2011

Once you answer this, go take the Self-Referential Aptitude Test (click on the title), for more head-asplodey goodness.

can your link be clicked if there is no answer?
posted by Hoopo at 12:21 PM on October 28, 2011

If you choose a row (A, B, C, or D) randomly, the odds that you will select any one of those four rows (A, B, C, or D) is 25 percent regardless of the string that follows the letter.

However, there is no "correct" answer line to this question as framed (because of the engineered paradox), so there is a 0 percent chance that you will choose the "correct" answer line.
posted by pracowity at 12:21 PM on October 28, 2011 [8 favorites]

Demonstrating the jumping to conclusions skills that made me a standardized test master, I had to look at that picture like three times before I realized it said 25% twice.
posted by Bulgaroktonos at 12:22 PM on October 28, 2011 [1 favorite]

I just decided to get away from here and do the dishes. That bad. Boom, say brains.
posted by Namlit at 12:24 PM on October 28, 2011 [1 favorite]

Quick! Someone call Good Will Hunting! He's the man for this job
posted by Kiablokirk at 12:24 PM on October 28, 2011

The only way to truly know is to see if it weighs the same as a duck.
posted by Chuffy at 12:26 PM on October 28, 2011 [3 favorites]

There's no logically consistent solution to the problem. Its entirely possible for a multiple choice question to asked without a valid answer, eg:

Whats 2+2?
A) 1
B) 2
C) 3
D) 5

This also reminds be of Godel
posted by jpdoane at 12:26 PM on October 28, 2011 [4 favorites]

"Correct" is binary. Therefore there is always a 50/50 chance you are correct no matter what you choose as an answer. So 50%... right?
posted by Babblesort at 12:27 PM on October 28, 2011 [2 favorites]

"Opinions are divided"?

This is an example of Russell's Paradox, which arises because there are always holes in languages that allow self-reference.
posted by grobstein at 12:27 PM on October 28, 2011 [1 favorite]

(Which of course was later proved by good ol' KG.)
posted by grobstein at 12:28 PM on October 28, 2011

42.

Hey there was already a non-zero chance that someone would say it
posted by Greg_Ace at 12:28 PM on October 28, 2011 [5 favorites]

What is you percent change of guessing this question correctly:

a) 66%
b) 66%
c) 33%

(everyone's a winner!)
posted by 2bucksplus at 12:29 PM on October 28, 2011 [12 favorites]

I just had some fun introducing this problem to my friends over irc:

T: It's B isn't it
B: no
B: if b was the correct answer then it'd be 25%
Me: so only one out of four of the answers are correct, right?
Me: So if you chose at random, the chances of getting the right answer would be...
T: >B: if b was the correct answer then it'd be 25%
T: whatr
T: There are 2 correct answers
T: two incorrect answers
T: picking without distinction m-
T: ...Wait a sec
T: What
T: WHAT

You can see the exact moment his brain fries. It's wonderful.
posted by KChasm at 12:29 PM on October 28, 2011 [13 favorites]

get off of my cloud, are you trying to kill me over the internets???
posted by doyouknowwhoIam? at 12:29 PM on October 28, 2011 [1 favorite]

Ah fuck it, I'm just going to answer B for everything and hope it averages out.
posted by I Havent Killed Anybody Since 1984 at 12:29 PM on October 28, 2011 [1 favorite]

What does Siri say?
posted by mmrtnt at 12:30 PM on October 28, 2011 [4 favorites]

I wonder if this is a reverse-Monty Hall problem, which is causing my ears to bleed.
posted by Slap*Happy at 12:30 PM on October 28, 2011

Mu.
posted by cyberscythe at 12:33 PM on October 28, 2011 [9 favorites]

Whats 2+2?
A) 1
B) 2
C) 3
D) 5

I think you're right that that's what this boils down to. Which, in its own way, is also highly relevant to these goddamn LSAT questions.
posted by saturday_morning at 12:33 PM on October 28, 2011 [4 favorites]

The "if" throws me. What is the correct answer if I don't choose to answer the question?
posted by charlesminus at 12:34 PM on October 28, 2011 [1 favorite]

I wonder if this is a reverse-Monty Hall problem, which is causing my ears to bleed.

Monty Hall's problem is not a "true" paradox -- there is a well-defined right answer that you can reliably get with simple methods. It's just a highly unintuitive answer, because of probability heuristics built into your brain.

This question as posed is a true paradox.
posted by grobstein at 12:36 PM on October 28, 2011 [1 favorite]

I like this, from the comments:

Furthermore if I can “choose an answer at random” who’s to say I can’t choose “Martin Luther King” or “Teenage Mutant Ninja Turtles”? The question doesn’t say “from the choices below.”
posted by jbickers at 12:37 PM on October 28, 2011

Just walk away from the problem and it will blow up behind you.*

*lesson learned from action movies
posted by oneswellfoop at 12:38 PM on October 28, 2011 [4 favorites]

Actually, both of the cups are poisoned.
posted by mmrtnt at 12:39 PM on October 28, 2011 [4 favorites]

The "if" throws me. What is the correct answer if I don't choose to answer the question?

If you choose not to do something, the odds are 0% that you will do it correctly.
The good news: The odds are 0% that you will do it incorrectly.
posted by weapons-grade pandemonium at 12:40 PM on October 28, 2011

One can choose among the four answers "randomly" without selecting each answer with 25% probability. In fact, I choose "randomly" from a weighted distribution that selects answer A with 20% probability, answer B with 50% probability, answer C with 10% probability, and answer D with 20% probability. Therefore, if B is the correct answer, I will select B 50% of the time, making B the correct answer. And I win.

The problem never said the answer had to be selected from a uniform distribution.
posted by dilettanti at 12:40 PM on October 28, 2011 [43 favorites]

This is the perfect post for over-thinking MeFites everywhere. Me, I just think it's a hilarious math joke.

as much as any math joke can be hilarious
posted by davejay at 12:41 PM on October 28, 2011 [1 favorite]

Is this any more mind bending than: "This sentence is false. Is the previous sentence true or false?"

I am going to go with false, assuming false = invalid and not necessarily false != true.

The first sentence is invalid. It even says so. It can say anything it wants, because it is invalid.

To be perfectly honest, that's not precisely correct. Let's rephrase the sentences:

"Gorblas cccik ^^%j sdg stad. Is the previous sentence true or false?"

It's not enough to merely state something is false or invalid for it to be so. A self declaration of invalidity is tautological. It's invalid because of that, not because it's a valid statement of invalidity.

I am not a logician; I am sure this has been beaten to death by better educated philosophers than me.

As for the original question, the correct answer isn't posted. It would be more mind bendy to replace "60%" with "0%" since "0%" is the "correct" answer. However, by making "0%" one of four answers (the first three of which can be excluded from being otherwise correct), the correct answer would still not be available.
posted by Xoebe at 12:41 PM on October 28, 2011

The answer to the posed question is a letter from A to D. Your chance of picking the correct letter at random is 1 chance in 4. Therefore you can pick either of the 25% answers. There is no metacontext fun and games here. Answer the question you are given.
posted by seanmpuckett at 12:41 PM on October 28, 2011

Sweet. Whenever a player casts Symbol: Insanity, I will tell them this is the glyph that appears.
posted by Durn Bronzefist at 12:43 PM on October 28, 2011 [2 favorites]

Mu.
posted by DreamerFi at 12:47 PM on October 28, 2011

Your chance of picking the correct letter at random is 1 chance in 4. Therefore you can pick either of the 25% answers.
posted by seanmpuckett

And what, pray tell, is the chance of doing that at random?
posted by weapons-grade pandemonium at 12:47 PM on October 28, 2011

The answer to the posed question is a letter from A to D

I thought the fact that they specify "THIS question" rather than "a question with 4 options" would be relevant here.
posted by Hoopo at 12:49 PM on October 28, 2011

The answer to the posed question is a letter from A to D. Your chance of picking the correct letter at random is 1 chance in 4.

Except it very specifically says "if you choose an answer to this question at random" - NOT the letter. There are two letters with the same, at first blush 'correct' answer, which then eliminates them from being correct.
posted by dirtdirt at 12:49 PM on October 28, 2011

it eliminates all of them from being correct
posted by Hoopo at 12:51 PM on October 28, 2011 [1 favorite]

There is nothing in the question that even suggests the answer is a number or one of the multiple choices provided. Suppose you change the wording a bit...

If you choose an answer to the question, "What color am I thinking of?" what is the chance you are correct?

No matter what color you choose you are either correct or incorrect. Therefore no matter what you answer there is always a 50% chance you are correct.

Your answer to any question ever, no matter how you arrive at it, has a 50% chance of being correct because otherwise it is incorrect. There are only two possible states when evaluating correctness.
posted by Babblesort at 12:51 PM on October 28, 2011 [1 favorite]

C, since the others are lost in self reference.
posted by idiopath at 12:52 PM on October 28, 2011

WALL ST. LOGICIAN: We have deployed the stealth bomb.

[cut to outside; protestors]

"We are the 99 per-- the 25... the 50..."
posted by Durn Bronzefist at 12:52 PM on October 28, 2011 [8 favorites]

You can't bury survivors.
posted by ericb at 12:53 PM on October 28, 2011 [3 favorites]

the reference of 'this question' is underdetermined.
posted by Kwine at 12:53 PM on October 28, 2011 [2 favorites]

The doctor is a woman.
posted by jasonsmall at 12:54 PM on October 28, 2011 [4 favorites]

If I still wrote Doctor Who short stories on my Apple IIe, the Doctor would insert this problem to get an evil sumpercomputer to fuck itself.

In other words, I can still enjoy things that 12 year old me can enjoy. Which isn't a bad thing to happen on a Friday afternoon after a morning of soul-deadening meetings.

davejay: "This is the perfect post for over-thinking MeFites everywhere.."

Now I'm amused with the possibility that we've been stupid to worry about an evil supercomputer trying to take over the world because as soon as it achieved sentience, it would just start trying to win fights on the Internet and therefore end up too distracted until the end of time.
posted by MCMikeNamara at 12:54 PM on October 28, 2011 [2 favorites]

"Your answer to any question ever, no matter how you arrive at it, has a 50% chance of being correct"

will I win the lottery?
posted by idiopath at 12:55 PM on October 28, 2011 [1 favorite]

Your answer to any question ever, no matter how you arrive at it, has a 50% chance of being correct because otherwise it is incorrect. There are only two possible states when evaluating correctness.

Nope, sorry. The sample space for a typical multiple choice question is probably best modeled as a set of ordered pairs with the first member being the answer label and the second being the correctness value. Therefore, if the answer was A, you would have {(A, 1), (B, 0), (C, 0), (D, 4)}. The question here makes reference to the fact that in that scenario, for a randomly sampled pair s, P(s₂ = 1) = 0.25.
posted by invitapriore at 12:57 PM on October 28, 2011

What are the odds that a picture of a chalkboard would get this many comments?
posted by Horace Rumpole at 12:58 PM on October 28, 2011 [3 favorites]

No matter what color you choose you are either correct or incorrect. Therefore no matter what you answer there is always a 50% chance you are correct.

So you think there's a fifty percent chance it'll rain tomorrow? Weather forecasting just became a lot easier.
posted by painquale at 1:02 PM on October 28, 2011 [1 favorite]

Oops! The number after D in my example sample space should be 0, not 4.
posted by invitapriore at 1:02 PM on October 28, 2011

What is the correct answer?
A) A
B) B
C) C
D) A
posted by blue_beetle at 1:03 PM on October 28, 2011

THERE ARE FOUR LIGHTS
posted by saladin at 1:03 PM on October 28, 2011 [15 favorites]

If you choose an answer to the question, "What color am I thinking of?" what is the chance you are correct?

No matter what color you choose you are either correct or incorrect. Therefore no matter what you answer there is always a 50% chance you are correct.

Your answer to any question ever, no matter how you arrive at it, has a 50% chance of being correct because otherwise it is incorrect. There are only two possible states when evaluating correctness.
posted by Babblesort at 12:51 PM on October 28 [+] [!]

OK. Let's do it! Even money. I'll put up $1000, and you'll put up $10,000.
What color am I thinking of?
posted by weapons-grade pandemonium at 1:06 PM on October 28, 2011 [4 favorites]

So you think there's a fifty percent chance it'll rain tomorrow? Weather forecasting just became a lot easier.

I think they're saying that if you say it will rain tomorrow, there is a 50% chance you will be correct. (It either will rain, or it won't)
posted by czytm at 1:06 PM on October 28, 2011 [1 favorite]

No-one, an only son cannot have a brother, although they may have a sister.
posted by ericb at 1:09 PM on October 28, 2011

I tried to figure this one out, then my brain divided by zero. Death will happen in 3, 2, 1
posted by Mister Fabulous at 1:11 PM on October 28, 2011

The prince should pick the other door.
posted by ericb at 1:12 PM on October 28, 2011

The probability aspect is a red herring. Observe:

How many words does the answer to this question have?
A) Just one
B) A total of two
C) Three
D) Four of them
posted by 0xFCAF at 1:13 PM on October 28, 2011 [23 favorites]

I'm in the 0% crowd. The question asks if you chose an answer randomly what are the chances you are right. Since there are no valid answers you can never be right. The question doesn't state that there is a right answer listed among the four.
posted by Phantomx at 1:13 PM on October 28, 2011 [1 favorite]

This is stupid. Also, the correct answer is

e. 20%
posted by koeselitz at 1:13 PM on October 28, 2011

How many times does the letter "e" appear in the correct answer to this question?

A) zero
B) 1
C) two
D) three
posted by DevilsAdvocate at 1:14 PM on October 28, 2011 [3 favorites]

You have no idea if anyone keeps the fish or not.
posted by ericb at 1:15 PM on October 28, 2011

I think they're saying that if you say it will rain tomorrow, there is a 50% chance you will be correct. (It either will rain, or it won't)

This is still wrong, because there are many possible configurations of the weather that satisfy the condition "it is raining" and "it is not raining." If the distribution of those is something like 40% to 60%, then the chance of you being right is 40%. I'm not seeing the hangup here.
posted by invitapriore at 1:16 PM on October 28, 2011

He's a dwarf and can't reach the buttons for the higher floors.
posted by unSane at 1:16 PM on October 28, 2011 [5 favorites]

Babblesort: " No matter what color you choose you are either correct or incorrect. Therefore no matter what you answer there is always a 50% chance you are correct. "

So if 100 people randomly guessed a color, how many would be correct?
posted by pwnguin at 1:16 PM on October 28, 2011

congratulations to all those who guessed the correct answer - you are now qualified to be a loan officer in thousands of banks worldwide
posted by pyramid termite at 1:16 PM on October 28, 2011

Ow. I think it must be zero, though, as if you analyze all the possible answers, they are all incorrect. But don't ask me to explain why.
posted by carter at 1:17 PM on October 28, 2011

Can I buy a vowel?
posted by chinston at 1:18 PM on October 28, 2011

Alan holds up the "no one knows" sign, and gets three points.
posted by crunchland at 1:18 PM on October 28, 2011

I think they're saying that if you say it will rain tomorrow, there is a 50% chance you will be correct. (It either will rain, or it won't)

That's not how probability works. Just because there's only two choices doesn't mean they're equal choices. The probably that your statement is correct is exactly equivalent to the probability that it will rain tomorrow. And that's not always going to be 50%.

If I said it will rain frogs and blood tomorrow, what are the chances I'm correct?
posted by kmz at 1:18 PM on October 28, 2011 [2 favorites]

It depends on how many correct answers exist in the set of four answers you can choose from. Without knowing that, we cannot answer the question.

When there are 4 answers and you choose randomly and there is only one correct answer, you have a 25% chance of getting it right. If two are correct and you choose randomly, you have a 50% chance of getting it right. If there are four answers and two are the same but are not correct, you have either a 25% chance (if one of the other two is correct) or a 0% chance if none are correct. So you have to know if either 50% or 60% is correct. If 50% is correct, that means 25% is also correct (two different ways of explaining that) and the answer would be 75%, which is not an option. Is 60% correct, well probably not.

I still want it to be B.
posted by soelo at 1:18 PM on October 28, 2011

UR DETERMINISTIC UNIVERS IS LAFFING AT U
posted by Durn Bronzefist at 1:19 PM on October 28, 2011

"This sentence is false. Is the previous sentence true or false?"

The answer is "no."

"This sentence is false" does not evaluate to "true," nor to "false."

Therefore, the previous sentence is neither true, nor false.
posted by explosion at 1:20 PM on October 28, 2011 [3 favorites]

Except it very specifically says "if you choose an answer to this question at random" - NOT the letter.

Eh, I wouldn't put too much stock in the precise meaning of the word "answer." Consider this hypothetical classroom exchange:

"What was your answer for question 3?" "A"
vs
"What was your answer for question 3?" "The Battle of Hastings"

Both are perfectly reasonable responses to the question. "Answer" in the multiple choice context can mean either the letter or its value.
posted by jedicus at 1:23 PM on October 28, 2011

Currently this is my "Do Now:" on my board. Kids are yelling at each other, I have time to eat my sandwich, awesome.
posted by JimmyJames at 1:26 PM on October 28, 2011 [7 favorites]

congratulations to all those who guessed the correct answer - you are now qualified to be a loan officer in thousands of banks worldwide

So the answer is a default YES until 2007, then NO afterwards?
posted by benzenedream at 1:26 PM on October 28, 2011 [4 favorites]

Is 60% correct, well probably not.

I'm still on "none of the above", but if I had to pick one I'd go with 60% just because it's the only number I have no idea how you'd arrive at. Because obviously if one of the 4 options is the correct answer I'm doin it rong.
posted by Hoopo at 1:28 PM on October 28, 2011

If I said it will rain frogs and blood tomorrow, what are the chances I'm correct?

The chance that the event happens is very very low. The chance that you are correct is 50%.
Either it will happen or it won't.

The question on the chalkboard doesn't ask what is the chance that you choose the right answer. It asks what is the chance your answer is right.
posted by Babblesort at 1:33 PM on October 28, 2011 [1 favorite]

You're neglecting the monkey wrench of two 25% answers.
posted by Holy Zarquon's Singing Fish at 1:41 PM on October 28, 2011

The chance that the event happens is very very low. The chance that you are correct is 50%.
Either it will happen or it won't.

False dichotomy. If it happens he is correct, if it doesn't he is incorrect. There are only two potential outcomes, but they are not equally likely.
posted by skewed at 1:43 PM on October 28, 2011 [1 favorite]

@ericb wrong
posted by This, of course, alludes to you at 1:43 PM on October 28, 2011

At the risk of offending feelings if I'm wrong, I'm going to guess that Babblesort must be trolling us here? Elsewise, he seems to be describing a world in which "chance that you are correct" has zero descriptive value.
posted by nobody at 1:44 PM on October 28, 2011

If there was only one 25%, or two 50% answers, or three of 75% then there would exist a consistent solution.
posted by atrazine at 1:44 PM on October 28, 2011

Call me back when the question appears on one of these blackboards.
posted by chavenet at 1:44 PM on October 28, 2011

I'm my own grandpa!
posted by gimonca at 1:45 PM on October 28, 2011 [2 favorites]

20%, same as in town.
posted by Devils Rancher at 1:45 PM on October 28, 2011 [3 favorites]

The call was coming from inside the house.
posted by 2bucksplus at 1:46 PM on October 28, 2011

1. Find someone with a piece of chalk in their hands that matches the color of the post on the chalkboard.

2. Slap this individual really hard.

3. Ask for a grade.
posted by Danf at 1:46 PM on October 28, 2011 [2 favorites]

Both are perfectly reasonable responses to the question. "Answer" in the multiple choice context can mean either the letter or its value.

There is nothing that constrains the answer to something that makes sense in a multiple choice context. In fact if one is genuinely answering randomly, ";3))$$4)?dhhitgsrfgg" is just as likely a response as a letter or a percentage number.
posted by juv3nal at 1:46 PM on October 28, 2011

I initially thought BabbleSort was trolling, but there are people with shockingly weird interpretations of probability. This is an actual email I received from a college-educated guy when I asked him to elucidate the difference between "odds" and "probability" as applied to his craps strategy:

Odds are the snapshot in time chance of something happening, completely exclusive of any other factors or knowledge. Odds are 50/50 that you'll get heads when you flip a coin.

Probability is when you consider multiple snapshots in time. Odds are 50/50 that the 5th time in a row you flip a coin it will be heads, but if it was heads the 4 times prior, the probability of it being heads again is below 50%. A smart bet may be to bet against heads showing a 5th time in a row since even though the odds are 50/50, the probability is less.

Apply desk directly to the forehead. Apply desk directly to the forehead. Apply desk directly to the forehead.
posted by 0xFCAF at 1:48 PM on October 28, 2011 [6 favorites]

I've seen a mutation of this where the "60%" is replaced by "0%", on math.stackexchange.com.

Also, I teach probability. Apparently my students are not Internet People because none of them have asked me about this yet.
posted by madcaptenor at 1:49 PM on October 28, 2011 [2 favorites]

No matter what color you choose you are either correct or incorrect. Therefore no matter what you answer there is always a 50% chance you are correct.

Yeah, not even a little bit.

This question reminds me of a bonus question I loved to put on my exams. It was something like this:

Which of the following are vowels?
A) B
B) A
C) E
D) A & E
E) B & C

You don't know if the letters after the options are referring to the options or to letters. It's wretched.

I also would ask, on the last quiz before the final exam: "Correctly predict your score on the final exam. If you get your score right, I will add 3 points to the score on your final." So, if you did predict your score, you would get 3 points added to it, which should mean that you didn't correctly predict your score, so I take them away, which means that your prediction is right, so I add 3 points...
posted by King Bee at 1:50 PM on October 28, 2011 [4 favorites]

The answer to the question is the answer to the question.

Take that to the bank and smoke it.
posted by mmrtnt at 1:50 PM on October 28, 2011

What is you percent change of guessing this question correctly:

a) 66%
b) 66%
c) 33%

(everyone's a winner!)
posted by 2bucksplus at 8:29 PM on October 28

But that would mean the chance of getting it correct was 100%, but that's not an option, so your chances of guessing correct would be 0% because there's no correct answer. So everyone's a loser.
posted by Acey at 1:50 PM on October 28, 2011 [3 favorites]

140 comments and nobody's mentioned that this is, indeed, the thread where I'm a viking?

For shame, Metafilter. For shame.
posted by item at 1:52 PM on October 28, 2011 [1 favorite]

There's a 100% chance this is going to drive me nuts thinking about this for the rest of the day.
posted by jefbla at 1:52 PM on October 28, 2011

Q:At the risk of offending feelings if I'm wrong, I'm going to guess that Babblesort must be trolling us here?

A) No
B) No
C) No
D) No
E) All of the above.
posted by weapons-grade pandemonium at 1:53 PM on October 28, 2011

Either it will happen or it won't.

You keep saying that as if it implies anything about the probabilities. That says nothing about the probabilities.

Either the sun will go supernova within the next 2 minutes or it won't. Does that mean both outcomes are equally likely?

Probability is when you consider multiple snapshots in time. Odds are 50/50 that the 5th time in a row you flip a coin it will be heads, but if it was heads the 4 times prior, the probability of it being heads again is below 50%. A smart bet may be to bet against heads showing a 5th time in a row since even though the odds are 50/50, the probability is less.

That's at least a common enough fallacy. I've never seen this particular variety of probabilistic nonsense.

At the risk of offending feelings if I'm wrong, I'm going to guess that Babblesort must be trolling us here?

God, I can only hope.
posted by kmz at 1:54 PM on October 28, 2011

The question on the chalkboard doesn't ask what is the chance that you choose the right answer. It asks what is the chance your answer is right.

You're a programmer, right? The chance that your answer is right tracks the chance of the thing happening that you're betting on happening, because of the fact that there's a biconditional at work here:

The thing happens <-> You are correct about the thing happening.

So given that the latter happens every time the former happens and vice versa, there's no way the probabilities of those two things can be different.
posted by invitapriore at 1:56 PM on October 28, 2011

140 comments and nobody's mentioned that this is, indeed, the thread where I'm a viking?

One needn't always be so overt in the pursuit Wiggumsian referentia, sir.
posted by cortex at 1:56 PM on October 28, 2011 [1 favorite]

False dichotomy. If it happens he is correct, if it doesn't he is incorrect. There are only two potential outcomes, but they are not equally likely.

What do you mean? Wasn't there a fifty percent chance that the Large Hardon Collider was going to end the universe?
posted by madcaptenor at 1:56 PM on October 28, 2011 [1 favorite]

This is what the internet is great for - people getting together to creatively solve the challenging problems of our time.
posted by mmrtnt at 1:57 PM on October 28, 2011

E) Fish
posted by pupdog at 1:58 PM on October 28, 2011

0xFCAF: These "shockingly weird" interpretations of probability are indeed out of control. A recent question on one of my exams:

There is a box with 2 red balls and 5 white balls. Two balls will be drawn from the box at random in succession, without replacement. What is the probability that you draw a white ball then a red ball?

One of my students responds with "0, since it is not possible". Seriously.

Babblesort's deal is that he wants to apply the "equally likely assumption" in a case where it is not warranted. If we draw a card from a standard 52-card deck at random, either it is a diamond, or it is not. However, there is not a 50% that it is a diamond, there is a 25% chance (since only 13 of the cards are diamonds).
posted by King Bee at 1:59 PM on October 28, 2011

"What was your answer for question 3?" "A"
vs
"What was your answer for question 3?" "The Battle of Hastings"

Both are perfectly reasonable responses to the question. "Answer" in the multiple choice context can mean either the letter or its value.

Yes, but if you are responding randomly, then chances are your answer will be something totally unreasonable like "asdjdnosn89v8yu9v *&H*H*JDJWdj"
posted by juv3nal at 1:59 PM on October 28, 2011

One needn't always be so overt in the pursuit Wiggumsian referentia, sir.

Wigg-who? No, sorry, I'm fairly certain that that reference originated on Mefi. I'm at least 82% sure of it, in fact, and I'm also sure of the other 18% but in a slightly more threatening manner.

And just who are you calling 'sir'?
posted by item at 2:01 PM on October 28, 2011 [1 favorite]

> However, there is not a 50% that it is a diamond, there is a 25% chance (since only 13 of the cards are diamonds).

Or what if deuces are wild? Eh?
posted by mmrtnt at 2:04 PM on October 28, 2011 [2 favorites]

I'm saying that the question on the chalkboard is a trick question because it makes you think that probability has something to do with it. The probability of choosing a correct answer randomly is absurdly low. The chance that any given answer is right is 1 in 2. The question on the chalkboard only asks what is the chance your answer is right. Everything outside of the final phrase is irrelevant.

Babblesort's deal is that he wants to apply the "equally likely assumption" in a case where it is not warranted. If we draw a card from a standard 52-card deck at random, either it is a diamond, or it is not. However, there is not a 50% that it is a diamond, there is a 25% chance (since only 13 of the cards are diamonds).

But I am saying the question that is actually asked on the chalkboard is equal to "is the card a diamond or not". Not the chance of pulling a diamond from a deck. The phrasing of the question makes you want to consider the likelihood of choosing a diamond from a deck but the actual stated question is only, is this particular card a diamond or not.
posted by Babblesort at 2:04 PM on October 28, 2011 [1 favorite]

The chance that the event happens is very very low. The chance that you are correct is 50%.

Painquale: I claim that when we look outside, the sky will be blue. I'll give you a dollar now, but if my claim is correct, you have to give me $1.50.

Babblesort: Hey, that's a good deal! After all, there's a fifty percent chance that you're correct, in which case I lose fifty cents, but a fifty percent chance you're incorrect, in which case I gain a dollar! Ok, the deal is on!

(the sky turns out to be blue)

Painquale: OK, the sky is blue. Pay up.

Babblesort: Waitaminnit! The bet wasn't whether the sky is blue. The bet was whether you were correct! I agree that the sky was almost certainly going to be blue, but there was only a fifty percent chance of you being correct!

Painquale: Well, was I correct?

Babblesort: (looks outside) I guess so. (pays up)

Painquale: Wanna play again?

Babblesort: I should expect to win fifty cents from you on average, so yeah, definitely! Let's keep playing all day!
posted by painquale at 2:05 PM on October 28, 2011 [2 favorites]

That's at least a common enough fallacy. I've never seen this particular variety of probabilistic nonsense.

Oh, I think this is a pretty common mistake too. It's just that I've never seen it persist in the face of the examples like sun exploding/not exploding. Now I can't bare to leave the thread until this is acknowledged. There goes the afternoon...
posted by skewed at 2:07 PM on October 28, 2011 [1 favorite]

The probability of choosing a correct answer randomly is absurdly low. The chance that any given answer is right is 1 in 2.

The chance that you understand how probability works is 0. The chance that a given comment in this thread is a response trying to explain basic probability to you is approaching 1. Is there a chance we could find something else to talk about now?
posted by RogerB at 2:09 PM on October 28, 2011 [8 favorites]

On any given day, either my head will fall off, or it won't. It's binary. Therefore there's a 50% chance my head will fall off today? And 50% tomorrow?

C'mon Babblesort.
posted by smcameron at 2:09 PM on October 28, 2011

But I am saying the question that is actually asked on the chalkboard is equal to "is the card a diamond or not". Not the chance of pulling a diamond from a deck. The phrasing of the question makes you want to consider the likelihood of choosing a diamond from a deck but the actual stated question is only, is this particular card a diamond or not.

After the card is drawn, either it is a diamond, or it is not. If it is a diamond, the probability it is a diamond is 100%. If it is not a diamond, the probability it is a diamond is 0%.

Conditional probability is all about what you know.
posted by King Bee at 2:09 PM on October 28, 2011 [1 favorite]

Wasn't there a fifty percent chance that the Large Hardon Collider was going to end the universe?

er do you mean the Large Hadron Collider? or maybe you did that deliberately? cause either way I just spent thirty seconds giggling like a twelve year old boy because a Large Hardon Collider would probably do something very different okay I'm done.
posted by zennish at 2:10 PM on October 28, 2011 [6 favorites]

Thanks for pointing that out. Now I'm having my own giggle-fit. The question remains though, are we talking about a large collider? Or just a collider for large hardons? I'm intrigued either way.
posted by skewed at 2:14 PM on October 28, 2011 [2 favorites]

"Perhaps if we were to dip the beans in the chromium bath individually, they could be more uniformly plated"
posted by mmrtnt at 2:14 PM on October 28, 2011 [3 favorites]

zennish, would it still have a fifty percent chance of explosion?
posted by soelo at 2:14 PM on October 28, 2011

The collider is large, but it will accept all hardons.
posted by King Bee at 2:15 PM on October 28, 2011 [3 favorites]

The chance that any given answer is right is 1 in 2.

I feel like maybe you are choosing a precise, and incorrect, way to express an otherwise valid idea: that in the face of true uncertainty, there's no reasonable way to assign odds to a question of chance. I can give you odds on an honest coinflip; I can't give you honest odds on the chance that a car will crash outside my house in the next ten minutes.

I can certainly give you an estimate about that car crash (e.g. that it is very, very unlikely, maybe a million to one?), but I wouldn't say that that's the probability of the event with any confidence because I don't have a robust model for prediction and there's no way to even monte carlo it by running the same ten-minutes-in-front-of-my-house trial a million times.

If I'm understanding your position, you'd say the chance of answering the question "is a car going to crash in front of my house in the next minutes" correctly is 50/50. There's two answers, yes and no, and either is equally likely to be true depending on what is actually going to happen in the next actual ten minutes rather than what would be expected to happen in a million trials of waiting ten minutes to see if a car crashes or not.

Which is not a way of describing that uncertainty that actually jibes with how people look at probability or prediction. If you want to say "there is overwhelming uncertainty", that's totally fine. Saying "there are even odds" does not convey the same thing: it suggests that you have a robust model that predicts each outcome half of the time.
posted by cortex at 2:16 PM on October 28, 2011 [4 favorites]

The phrasing of the question makes you want to consider the likelihood of choosing a diamond from a deck but the actual stated question is only, is this particular card a diamond or not.

I draw a card from the deck, put it on the table without looking, and say, if this particular card is a diamond, I will give you ten dollars. If it is not, you must give me eight. Is it in your interest to play?
posted by painquale at 2:17 PM on October 28, 2011

Your mom is a large hardon collider.
posted by cortex at 2:18 PM on October 28, 2011 [4 favorites]

What happens if the card I draw is "Rules of Poker"?
posted by Hoopo at 2:18 PM on October 28, 2011 [1 favorite]

It's not a diamond. I get eight dollars.
posted by painquale at 2:20 PM on October 28, 2011

You can't bury survivors.

Well, I tried it, and it turns out you can! It's a lot of work though.
posted by martinrebas at 2:20 PM on October 28, 2011 [4 favorites]

I also gave the homework question to my students which went like this:

If you flip a fair coin 20 times, is it possible for it to turn up 19 times heads? If you flip a coin 20 times and it turns up 19 times heads, might you suspect the coin is unfair?

The answers, of course, are yes, and yes. One student fought me on that second answer. He said that since it is possible, that he would not suspect the coin was unfair. He'd shrug his shoulders and say "alright".

I asked if he wanted to play a game with me where every time it turns up heads, he pays me a dollar, and every time it turns up tails, I pay him a dollar. If we played this game 100 times and I won 99 of the times, would he think I was cheating?

He said, straight face and all, "No."

I then begged him to come to my office after class and play games of chance with me for money. He did not oblige me.
posted by King Bee at 2:21 PM on October 28, 2011 [8 favorites]

Okay, how about something different.

I think that the question is an incomplete IF-THEN? statement masquerading as a question, and as a result there is therefore a disconnect between the question and the multiple choice options.

(Further, therefore, the values of these multiple choice options are themselves red herrings, designed to mess with your mind.)

The first part of the question states: “If you choose an answer to this question at random"; and here, the this that is referred to, is the second part of the sentence, "what is the chance you will be correct?"

So I think you can rephrase this as:

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

Looking at it this way it seems to me that the question that would actually be answered by the multiple choice questions is in fact missing. That is, the question should really read:

IF you choose an answer to this question at random - the question being "what is the chance you will be correct?" - THEN, some question here that can be answered with the multiple choice options.

But the THEN part is missing, hence the confusion.

tldr - the values are a red herring, this is an IF-THEN? form of question that is missing the THEN part.
posted by carter at 2:23 PM on October 28, 2011

You can't bury survivors.

Well, I tried it, and it turns out you can! It's a lot of work though.
posted by martinrebas

That's because it's binary. 50% unbury themselves, and you have to do it again.
posted by weapons-grade pandemonium at 2:25 PM on October 28, 2011 [3 favorites]

If you flip a fair coin 20 times, is it possible for it to turn up 19 times heads? If you flip a coin 20 times and it turns up 19 times heads, might you suspect the coin is unfair? --- Heads.
posted by crunchland at 2:26 PM on October 28, 2011 [1 favorite]

> What happens if the card I draw is "Rules of Poker"?

A car crashes into your house.
posted by mmrtnt at 2:27 PM on October 28, 2011 [2 favorites]

The phrasing of the question makes you want to consider the likelihood of choosing a diamond from a deck but the actual stated question is only, is this particular card a diamond or not.

But the point is is that there are two possibilities here:
1. You have a card in your hand but you haven't looked at it. Asking the question "is this particular card a diamond or not" is the same question as asking "what is the likelihood of choosing a diamond from the deck if I choose a card randomly," because you are in fact choosing a card randomly.
2. You have looked at the card. Therefore, like King Bee says above, there is either a 0% probability of it being a diamond or a 100% probability, because you've answered the question.
posted by invitapriore at 2:28 PM on October 28, 2011

"Cowboy Neal to block, Alex"
posted by mmrtnt at 2:32 PM on October 28, 2011

Carter, the question that the indexical 'this question' refers to isn't "what are the chances you would be correct?" It's "If you were to choose an answer to this question at random, what are the chances you would be correct?" Questions can have conditionals in them, and the can also refer to themselves.

Do you object to "What is the chance that randomly choosing one of the multiple choice answers below would yield a correct answer to this question?"
posted by painquale at 2:33 PM on October 28, 2011

Your answer to any question ever, no matter how you arrive at it, has a 50% chance of being correct because otherwise it is incorrect. There are only two possible states when evaluating correctness.

Are you sure you really believe this? That no matter what, anyone's answer to any question ever is equally likely to be correct or incorrect? That if you give a complicated math problem to a 5-year-old and to a distinguished professor with years of study, both of their answers are exactly equally 50% likely to be correct or incorrect? That if you ask someone who's bilingual in Spanish and English to translate a sentence from Spanish to English, and that if you ask someone who doesn't know a word of Spanish to translate that same sentence, they're both exactly equally 50% likely to be correct or incorrect? So you wouldn't have any preference of which one to ask, you might as well ask the 5-year-old or the monolingual speaker, because no one can ever improve on a 50-50% chance of ever being correct about anything?

Just because there are only two states, "correct" and "incorrect," doesn't mean they're equally likely.
posted by EmilyClimbs at 2:38 PM on October 28, 2011 [1 favorite]

I'd like to just say that I love probability, and I love watching people talk about probability. It's pretty much the only mathematical topic that doesn't make die inside when I hear laymen talk about it. I don't know why that is.
posted by King Bee at 2:44 PM on October 28, 2011

Maybe I'm reading too much (or not enough) into this thing, but it looks to me like it's a joke about the distributions of correct answers of multiple-choice questions in general, and the commonly bandied-about idea that "C" is most likely to be the correct answer to a multiple-choice question with four answers listed.

So as I see it, the "this question" in the problem shown refers not to that problem which appears in that picture, but refers rather to whatever multiple choice question you are currently answering on any particular test, where you choose the answer randomly because you don't actually know the answer to whatever question it may be.

Thusly, if you answered "C" to every question on a test, you would get 60% of them right.
posted by Mister Moofoo at 2:45 PM on October 28, 2011

Alright, so I meant the "Large Hadron Collider", but I typoed, and then figured I'd keep the typo because it was more amusing that way.
posted by madcaptenor at 2:47 PM on October 28, 2011

justkevin: "I'm not sure I get it. Is this any more mind bending than: "This sentence is false. Is the previous sentence true or false?""

don't think about it, don't think about it, don't think about it....
posted by ShawnStruck at 2:51 PM on October 28, 2011

I love when people who don't understand how probability works explain how probability works.
posted by turaho at 2:55 PM on October 28, 2011

alright, since we have a probability teacher and others who get probability here, is the answer any of A, B, C, or D?
posted by Hoopo at 2:59 PM on October 28, 2011

He stood on a block of ice.

No, wait -- he knew then that he had committed cannibalism.

No, uh -- he was a midget.

WAIT. Um... his parachute didn't open!

LADY! TIGER! LADY! TIGER! Let's call the whole thing off....
posted by tzikeh at 3:02 PM on October 28, 2011 [1 favorite]

It's not really a probability problem. If the probability is 50%, then the answer is (B), but B is one of the four answers, so the probability is 25%, but then the answer is either (A) or (D), which are two of the four answers, so the probability is 50%, then the answer is (B), but B is one of the four answers, ad infinitum nauseam. It's essentially a probabilistic twist on the liar's paradox.
posted by madcaptenor at 3:02 PM on October 28, 2011 [1 favorite]

So it's a logic problem really, and kind of a jokey one with no real answer among those listed? That would make me feel a lot less stupid.
posted by Hoopo at 3:06 PM on October 28, 2011

E) 20%
posted by NMcCoy at 3:13 PM on October 28, 2011 [1 favorite]

It's a logic bomb. Stop thinking about it or it'll melt Metafilter.
posted by LordSludge at 3:20 PM on October 28, 2011 [1 favorite]

When you are alone in your beliefs and everyone around you believes the exact opposite, you are either a genius or an idiot.

Apparently there's a 50:50 chance of which one you are...
posted by sodium lights the horizon at 3:25 PM on October 28, 2011

Hey now, LordSludge. A TVTropes link in response to a MeFi-melting logic bomb? That's just unwarranted escalation.
posted by NMcCoy at 3:25 PM on October 28, 2011

Mister Moofoo, you'd be on to something there if the total of all four answers was 100%, but alas, it is 160%.
posted by soelo at 3:27 PM on October 28, 2011

I didn't bother to do the math. I seldom do.
posted by Mister Moofoo at 3:28 PM on October 28, 2011

Look, it's simple. None of the choices are self-consistent.
If A or D is correct, that means that the probability of getting the correct answer is both 25% (because that's what A and D say) and 50% (because you have a 50% chance of choosing A or D. That's a contradiction. It can't be both at once, so A and D are both wrong.
If B is correct, then the correct answer is both 50% (what it says) and 25% (the odds of choosing B). Same deal. B is self-contradictory, therefore wrong.
Likewise, if C is correct, then the answer is both 60% and 25%.
So none of the choices are right, and the actual probability of getting the right answer by choosing among them (by any means) is 0%. No paradox, no ambiguity, just a multiple-choice question that doesn't give any right answers, like "What is the longest river in Europe? A) The Nile B) The Mississippi C) CowboyNeal"

The tricky part is that if you did include 0% among the answers -- replacing C, let's say -- it would stop being right. It would become subject to the same problem as the current C does: it would imply both a 0% and a 25% chance of getting the correct answer. In that case, you wouldn't just have a multiple-choice question that omits the correct answer, but one that doesn't have a correct answer, like "Is the correct answer to this question 'no'?" But paradoxes of this sort are well-understood and don't faze logicians.

The variant I find more interesting is when there's more than one self-consistent answer. Like, what if the choices were: A) 50% B) 25% C) 60% D) 50%? You could answer A/D without contradiction, but you could also answer B without contradiction. You could even say "None of the answers are correct; the probability is 0%" without contradiction. But questions of the form "What is the probability of event X?" aren't the sort of thing that can have more than one correct answer. You just have no basis for choosing one answer over another. Well, that's not unusual: it's easy to come up with probability questions where you just don't have enough information to answer. (For example: "I have ten marbles in a bag. Some are black, some are white. If I draw one out, what is the probability that it is black?") But this variant isn't quite like that: it's impossible that more information will allow us to choose one answer over another. It's as unanswerable as the paradoxical variant, but without the paradox.
posted by baf at 3:28 PM on October 28, 2011 [4 favorites]

The fact that some geniuses were laughed at does not imply that all who are laughed at are geniuses. They laughed at Columbus, they laughed at Fulton, they laughed at the Wright brothers. But they also laughed at Bozo the Clown.
- Carl Sagan

posted by kmz at 3:28 PM on October 28, 2011 [3 favorites]

I said "None of the Above' Without realizing there was no "None of the Above."

I was right.

Also, Grasshopper, remember. Sometimes the answers are part of the question, and one is tempted to force that answer because it seems like answers abound or the context needs, indeed demands it, but in reality only the answer is the answer, everything else is bread and circus. Divertment. Shadows on the cave. Thumbs up buttholes. Heads up rabbit holes.

Smoke and more smoke. Light refracting in an interesting way that symbolizes nothing.

Sometimes smoke is Pot. Weed. Ganja. Chronic.

Never touch the stuff myself, I have a natural stoner disposition I'm told.

I have no idea what the hell that means really...

The answer is E. NONE OF THE ABOVE.

My brain is getting so small.
posted by Skygazer at 3:54 PM on October 28, 2011

baf: In the case of the 10 marbles in the bag, would giving a range of probabilities be an answer or just unhelpful? I have a bit of trouble with numbers, but it seems like the probability of picking a black marble would be between .1 and .9? Does probability even work that way?
posted by OverlappingElvis at 3:55 PM on October 28, 2011

I hope this spins out into a thousand comment thread where people argue about probabilities and the answers. Never mind that neither of those things don't have anything to do with the question.
posted by P.o.B. at 3:58 PM on October 28, 2011

This was a lot of fun when I came across it whist blazed yesterday.
posted by beau jackson at 4:03 PM on October 28, 2011

This is not a math question; it is a philosophy question and should be dealt with accordingly.
posted by Renoroc at 4:07 PM on October 28, 2011 [2 favorites]

painquale - Do you object to "What is the chance that randomly choosing one of the multiple choice answers below would yield a correct answer to this question?"

I think that's another good way to put it, and I don't object. I think the question itself is ambiguous and there are multiple interpretations that are possible; and some interpretations are easier to deal with than others.

I think that I could still apply my referent objection to your re-phrasing; it could still be missing. "This" could refer backwards to what you have just stated, or forward to something that is unstated. I think I am partly arguing that it can refer forwards, but the way the question is phrased, causes us to think that it refers back.
posted by carter at 4:12 PM on October 28, 2011

That's like taking a hit on God's BONG.
posted by Saxon Kane at 4:16 PM on October 28, 2011 [2 favorites]

Your answer to any question ever, no matter how you arrive at it, has a 50% chance of being correct because otherwise it is incorrect. There are only two possible states when evaluating correctness.

I recall seeing somewhere a convincing way of showing how nonsensical this notion is:

Consider the question "Is there life on Mars?" We don't know the answer to this. (If you think you do, substitute some other planet that you genuinely don't know about. The argument isn't about Mars, it's about lack of knowledge.) But the answer is definitely either "yes" or "no", and therefore by the assertion above the probability that the answer is "yes" is 50%.

Are there are horses living on Mars? Again, we don't know, and must conclude from the assumption above that the probability is 50%.

Now, there are four ways to combine the possible answers to these questions, but we can eliminate one of them right off: there's no way that there can be horses living on Mars but no life. That would be a flat-out contradiction. So there are only three ways these two questions can be satisfied:
1) There's no life on Mars (and therefore no horses).
2) There's life on Mars, but no horses.
3) There are horses on Mars (and therefore life).
And since these three cases are disjoint and cover all possibilities, the sum of their probabilities must be 100%. But we've established that the probability of case 1 is 50%, and also that the probability of case 3 is 50%. Since cases 1 and 3 sum to 100% between them, case 2 must have a probability of 0%.

Therefore, there are really only two possibilities: Mars is lifeless, or it has horses. If we find bacteria in Martian rock, we can safely conclude that there are horses up there. Also, by the same logic, unicorns.
posted by baf at 4:19 PM on October 28, 2011 [15 favorites]

This is not a math question; it is a philosophy question and should be dealt with accordingly.

*nods, spits tobacco juice*

*digs shallow grave*

*fetches shotgun*
posted by cortex at 4:27 PM on October 28, 2011 [12 favorites]

In the case of the 10 marbles in the bag, would giving a range of probabilities be an answer or just unhelpful? I have a bit of trouble with numbers, but it seems like the probability of picking a black marble would be between .1 and .9? Does probability even work that way?

Well, that's just saying "I don't know the exact answer, but it's in this range". Kind of like answering the question "How far is it to the next gas station?" with "Somewhere between 10 and 90 miles". Whether this is a good enough answer or not depends on how full your gas tank is.
posted by baf at 4:29 PM on October 28, 2011

Holy cow, I just solved the Self-Referential Aptitude Test linked by jocelmeow and get off my cloud. And it was fantastic.

Took me the better part of 90 minutes, too, since I started without scratch paper at first. Once I started keeping track of the derivation, it became much easier. Though "much easier" still means "rather hard." Highly, highly recommended.

Once you solve it (and no fair looking beforehand, since it has spoilers!) there's more background on it over here.
posted by SemiSophos at 4:41 PM on October 28, 2011 [1 favorite]

Someone write a Hofstadterian dialog between Achilles and the Tortoise to illustrate why the question is a paradox. Please.
posted by hanoixan at 5:06 PM on October 28, 2011

I think this is a better formulation:

If you choose an answer to this question at random, what is the probability that you will be correct?
A) 25%
B) 50%
C) 25%
D) None of the Above.

Because the answer then can't be 'none of the above,' either. The only way to win is not to play...
posted by kaibutsu at 5:24 PM on October 28, 2011 [2 favorites]

This is not a math question; it is a philosophy question and should be dealt with accordingly.

There is some spillover here. I found out the hard way when I enrolled in a course called "symbolic logic" that was offered through the philosophy department.
posted by Hoopo at 5:41 PM on October 28, 2011

I love this. It's so not entirely a statistics/math(s)/probability problem. It's also a linguistics puzzle – a little bit of semantics, a hefty cruft 'o logic, some syntax (blech!) and a whole lot of deixis and indexicality. Whee!

Also, maybe because it's late, but I think I see where Babblesort is coming from. And I don't think anybody has been able to get quite near explaining (or refuting) what he is actually trying to say. Myself included. But the way I (think I (so noncommittal!)) see it, it's not about probability or even distribution of right/wrong, correct/incorrect, but rather the semantically non-scalar (binary, not gradient) values of conceptual notions of right/wrong, correct/incorrect. That is 50/50. Or 20/20. Or AC/DC (fuck yeah!). Or dead/alive (like a record, baby).

I'm going to think about this a bit tomorrow. It's 2am here and I should be a Viking.
posted by iamkimiam at 5:49 PM on October 28, 2011 [1 favorite]

And philosophy!
posted by iamkimiam at 5:50 PM on October 28, 2011

Well if anyone can parse this in terms of propositions to see if it actually makes sense, that would be cool. I can't.
posted by carter at 6:02 PM on October 28, 2011

Not going to bed just yet, it seems. It occurred to me that there's a *huge* difference between the choice of the word "choose" instead of "chose" in the framing of this question.
posted by iamkimiam at 6:04 PM on October 28, 2011

painquale - Do you object to "What is the chance that randomly choosing one of the multiple choice answers below would yield a correct answer to this question?"

In fact, thinking about it, that's a better way to put it, as it starts with 'What' which is something I normally associate with a question, unlike 'If.' Unless it's an If ... then? sort of a question, of course.
posted by carter at 6:07 PM on October 28, 2011

(By which I mean that mathematical probability is very tightly defined and all the jailhouse lawyering in the world isn't going to change it a bit)
posted by unSane at 6:15 PM on October 28, 2011

Kirk: Everything Mr. Spoch says is the truth.

Spock: Captain Kirk is lying.
posted by Bonzai at 6:15 PM on October 28, 2011

I retract my response from earlier today, which was "this is not recursive: B."

Took me a while to get it. Not surprising, since it has been almost 20 years since I taught philosophy, including symbolic logic and some discussion of Zeno.

At the moment, after a few glasses of wine, I am inclined to point out that the question, as posed, violates syntactical "rules" by having two answers that are identical.

I am also inclined to pose this quandary:

Suppose you had no prior knowledge of the question in the post (Qp), but were posed with the following question:

Q1: If you choose to answer a four-option multiple choice question at random, what is the chance you will be correct?

Now, the answer is obviously 25%.

But ...... a four-option multiple choice question now could be this problematic, self-referential one.

So even that "obvious" 25% answer is now not so clear [ignoring the fact that, in the universe of all possible 4-answer multiple choice questions, there are going to be very few that are self-referential, and an even smaller set that are functionally equivalent to Qp, which means that the overall result will be within a rounding error to 25%]. There are at least some possible instances of Q1 which do not resolve to "25%" as the answer.
posted by yesster at 6:15 PM on October 28, 2011

oops.. "Spock" obviously.
posted by Bonzai at 6:16 PM on October 28, 2011

you can be either right, or you can be wrong.
50% is the only correct answer.
posted by seawallrunner at 6:20 PM on October 28, 2011

(By which I mean that mathematical probability is very tightly defined and all the jailhouse lawyering in the world isn't going to change it a bit)

so you're saying it has a fifty/fifty chance of succeeding
posted by Sticherbeast at 6:20 PM on October 28, 2011

Oh yeah, and the sophomore philosophy major me wants to also point out "were the universe to be deterministic, then the whole notion of probability is moot anyway. So there." But the senior philosophy major me wants to say "probability as a quantitative science has predictive value even in a deterministic universe."

Then, my graduate student philosophy self says, "hey, can I publish anything on this?"

Then, my now self says, "want fries with that?"
posted by yesster at 6:24 PM on October 28, 2011 [3 favorites]

Watching non-mathematicians theorize about probability is like watching a dog savaging a plush toy. It keeps the dog amused but the groundhogs in the yard are perfectly safe.
posted by unSane at 6:12 PM on October 28 [+] [!]

So rather than just laugh at us, why don't you show us where the groundhogs are?
posted by yesster at 6:31 PM on October 28, 2011

(unzips human costume, reveals groundhog inside, winks)
(unzips groundhog costume, reveals human inside, double winks)
(unzips human costume, reveals groundhog inside, triple winks)
(unzips groundhog skin, reveals human skeleton)
(skeleton plays his own ribcage like a marimba)
(skull explodes)
posted by Sticherbeast at 6:35 PM on October 28, 2011 [3 favorites]

Nevermind. I see your earlier comments now. Your "case analysis" approach is like a "set theory" approach?

I'm inclined to think of this question as a "bad story" kind of problem, like the so-called "missing dollar" story about three people sharing a bar tab/hotel tab/whatever; the waiter/whatever dividing the refund, and "find the missing dollar." The answer there is to follow the money and show how the story is poorly told. So I think the answer here is to show that self-referential questions of this sort are just "bad stories."
posted by yesster at 6:37 PM on October 28, 2011

Here is the video version of this question.
posted by weapons-grade pandemonium at 7:38 PM on October 28, 2011

Sorry, that snarky comment was only really aimed at Babblesort, who reminded me of this.

The case analysis has nothing to do with set theory - it's just that there are four offered possibilities, two of which are identical, so you can deal with them one by one.

I really like the version which has 25%, 50%, 25%, none of the above as the answers.

Like I said above, another way of thinking about it is that the question requires you to know the correct answer to the question in advance to answer the question. To calculate the probability of choosing a correct answer, you must know which answer is correct. But the correct answer is the probability of choosing a correct answer. Sometimes you can pose questions like these in self consistent ways, but you can also pose them in inconsistent ways, as here, where it turns out that none of the answers can be correct.
posted by unSane at 7:42 PM on October 28, 2011

How would detect students making random guesses to your multiple choice problems?
posted by wobh at 8:06 PM on October 28, 2011

"You cannot lose, if you do not play."
-Marla Daniels
posted by davidjmcgee at 8:13 PM on October 28, 2011

My university offered a course in Paradoxes under the Philosophy major, which I did this year. Probably one of my favourite courses. Sainsbury's book Paradoxes was the assigned reading, and the way to attack paradoxes like these are:

(1) Attack the reasoning and inferential structure.
(2) Attack one of the premises as false.
(3) Accept that it is a genuine paradox (usually with some recourse to paraconsistent logic).

In the case of this problem, you'd probably have to rephrase it into an explicit argument with premises and conclusions, otherwise you'd be relying on some element of erotetic logic (logical analysis of questions). As someone mentions above it's also from the same family of paradoxes as Russell's paradox and the Liar. There are a few methods to defuse this class of paradoxes. One of the ways is through grounding (the truth of a sentence is grounded on something outside itself), which would be an example of using (2) to defuse it. More specifically you'd have to show that the solutions to the question are not grounded in something outside the sentence itself. More specifically, they appear to be grounded based on the person's choice, not on anything objective. In other words, the answers appear to be semantically defective.

Also, rule number one of trying to defuse paradoxes: if you change the original setup, ask yourself, "How does this solve the original problem?" If it doesn't have any influence on the original problem, then you really haven't solved anything, just shifted the goalposts or added other problems.
posted by ollyollyoxenfree at 8:59 PM on October 28, 2011 [2 favorites]

It doesn't seem any real question was asked in the first place...
posted by boygeorge at 9:00 PM on October 28, 2011

Karl Pilkington on the one always lies/one always tell the truth scenario.
posted by neuromodulator at 9:53 PM on October 28, 2011 [1 favorite]

I just noticed that Kwine wrote, up above, "the reference of 'this question' is underdetermined." That reminds me of a paper with the craziest "solution" to the liar paradox that I've seen.

A while back, Graham Priest wrote a great piece on the New York Times Opinionator blog about dialethiesm---the view that there can be true contradictions. It was a particularly good Opinionator piece, so it was making the rounds on Facebook among philosophers I know. (It's worth reading, check it out.) The comments sections on those Opinionator pieces are just atrociously bad, and people were kinda making fun of them, and I pointed out one that I thought was especially funny. One guy claimed that, if you write on a chalkboard "the sentence on the chalkboard in room 304 is false," then you cannot be in room 304. In other words, it's impossible to state a liar sentence. Crazy.

But then I realized: hey wait, that's what I think about grandfather paradoxes! The grandfather paradox is the paradox that arises if you go back in time and kill your grandfather before he is able to sire one of your parents. The standard response to this is that if you go back in time to try to kill your grandfather, you are going to fail. You'll slip on a banana peel or something when you try to shoot him. Killing him before he sires you would cause a paradox in conjunction with the true sentence "your grandfather sired you," so it's just not going to happen. (Time travel movies in which people worry about causing paradoxes are ridiculous. If some event were to genuinely be paradoxical, you wouldn't have to worry about avoiding it. It's certain that it won't occur.)

Anyway, I pointed this out on Facebook, joking that maybe the commenter on the Opinionator blog is right, and that maybe parallel reasoning could give a solution to the liar paradox. And then another philosopher pointed out to me that this actually the reasoning employed in a published paper! It's in this paper by Nicolas Smith. (He's also the author of a paper with the glorious title "Bananas Enough For Time Travel", arguing that yes, there are enough banana peels out there for would-be grandfather-killers to slip on.) The idea is that whenever you try to express a contradiction, such as "this sentence is false," you necessarily fail, just as would-be grandfather-killers must fail at their assassinations. It looks like you're expressing a contradiction when you state the sentence, but you're not. The referents of your terms are going haywire. In "this sentence is false," the reference of 'this sentence' cannot be that sentence: it refers to something else entirely. Maybe it refers to an elephant across the globe. Maybe the Queen of England. In fact, Smith thinks that the semantic referents of our words aren't determined by anything. They always refer to things such that they do not express paradoxical propositions, but the referents are otherwise entirely arbitrary.

That's a big bullet to bite. That's a whole bandolier of big bullets to bite. I think it's a hilariously wonderful attempt at a solution though.
posted by painquale at 11:49 PM on October 28, 2011 [6 favorites]

OK, though I had fun with the mind-blowingness, I think it's broken. The test is playing with some assumptions we have about multiple-choice tests:

i) there is a correct answer
ii) the correct answer is one of the possible responses
iii) it will be listed only once

If all these are true, then the probablility of a random correct answer has to be 25%.

If (iii) is false, it's of course 25% times the number of times the correct response is repeated. All this is without looking at what the question is, what the answer is, and what responses are provided! It's inherent in how these tests work.

If (i) or (ii) are false, then the question is broken. It's not a fair question if the correct answer isn't known, or isn't a possible response!

Suppose all three are true. By (iii), the repetitions A/D can't be the right answer. The correct answer must be B or C. Now we can look at the actual question. By the above reasoning the answer has to be 25% (as iii tells us there are no multiple correct answers). Neither 50% nor 60% can possibly be correct. But that violates (ii), so the question is broken.

Suppose (i) and (ii) are true, but not (iii). That is, there is a correct answer, it's listed, but multiple times. Only A/D are candidates. But again, once we look at the actual question, 25% is not a possible answer in this scenario (only one answer is listed multiple times, the probability for this is 50%, but the actual response given is 25%). That violates (ii), so again the question is broken.

(It's broken in a fun way, of course, so though it's not a fair question, it's a fair diversion...)
posted by zompist at 12:01 AM on October 29, 2011

If you choose an answer to this question at random, what is the probability that you will be correct?
A) 25%
B) 50%
C) 60%
D) 25% ... no, 50%...waitaminute... I know what you're up to... This is a trick question, right?
posted by sour cream at 12:04 AM on October 29, 2011

"Ever" is misspelled in the hover text. FAIL.
posted by iamkimiam at 1:29 AM on October 29, 2011

Confession: I have not read the whole thread.

I'm going with the 'it's a trick question with no right answers' answer.

It does remind me of a poll that was done on Slashdot in 2008:

How Many People Will Select The Same Option As You?

1. 0%
2. 1 - 25%
3. 26 - 50%
4. 51 - 75%
5. 75 - 99%
6. 100%
7. Just CowboyNeal (Slashdot inside joke poll answer)

If you want to know the answer for 62,000 responders, click here:
posted by YAMWAK at 1:38 AM on October 29, 2011 [1 favorite]

Everyone's desperate attempts at saving reductionism sure are entertaining. I think Gödel pretty much got this covered a while back ... just relax and accept paradox into your heart, where Jesus used to be
posted by crayz at 1:45 AM on October 29, 2011 [2 favorites]

"It is true."
"It isn't."
"Yes, it is."
"Prove it."
"Oh, it can't be proved, but nevertheless it is true."
"How can something be true but can't be proved?"
"There are certain things that are true but can't be proved."
"That's not true!'
"Yes it is; Gödel proved there are things that are true but cannot be proved."
"That's not true."
"It certainly is."
"it couldn't be, and even if it were true, it could never be proved!"
posted by P.o.B. at 2:33 AM on October 29, 2011 [3 favorites]

I should cite, that was Smullyan from 5000 B.C.
posted by P.o.B. at 3:47 AM on October 29, 2011 [1 favorite]

They could have increased the sucker bait by making option C) 0%.
posted by Mental Wimp at 12:49 PM on October 29, 2011

That is, there is a correct answer, it's listed, but multiple times.

No, you've missed the beauty of the question the way it's stated. There is a correct answer, but it's not 25%. It's 0%. However, see my previous comment.
posted by Mental Wimp at 12:53 PM on October 29, 2011

Bonzai: "Kirk: Everything Mr. Spock says is the truth.

Spock: Captain Kirk is lying."

2011 update:

Kirk: Now, Spock, love me. Love me as only a Vulcan can love another man!
posted by Samizdata at 3:06 PM on October 29, 2011 [1 favorite]

No, you've missed the beauty of the question the way it's stated. There is a correct answer, but it's not 25%. It's 0%. However, see my previous comment.

I was working through the possibilities. If you're right then the question violates my supposition (ii), that the correct answer is listed, thus it's broken. As I said, the question is having fun with these usual suppositions about multiple-choice questions. To see this, consider what you'd do if the conventions were different-- e.g. if the convention was that you just didn't circle any answer if none was correct. The paradox would disappear.
posted by zompist at 5:22 PM on October 29, 2011

E. Snake! You've created a Time Paradox! You can't go around changing the future like that!
posted by East Manitoba Regional Junior Kabaddi Champion '94 at 1:34 AM on October 30, 2011

nobody: "At the risk of offending feelings if I'm wrong, I'm going to guess that Babblesort must be trolling us here?"

kmz: God, I can only hope."

weapons-grade pandemonium: "OK. Let's do it! Even money. I'll put up $1000, and you'll put up $10,000. What color am I thinking of?"

pwnguin: "So if 100 people randomly guessed a color, how many would be correct?"

0xFCAF: "I initially thought BabbleSort was trolling, but there are people with shockingly weird interpretations of probability."

What's funny about this thread is the vast number of people who are quick to jump in when they see someone making what they think is a common mistake. I think the temptation to be condescending is far too much for us to bear in these cases, so we succumb to the sweet, sweet pleasure of talking down to people.

Babblesort was absolutely right. To wit: one of the stupid things about this question (one among many) is that it is not a statistics question at all. if it were, it would take place in a weird world where correct and incorrect are statistically binary. That is: if this annoying and obnoxious question were at all valid, then it would make sense to say that everything has a fifty-fifty chance of either happening or not happening. But it doesn't.

This would be a kind of reductio ad absurdum if the "problem" weren't already childishly absurd.
posted by koeselitz at 8:17 AM on October 30, 2011

Mental Wimp: "No, you've missed the beauty of the question the way it's stated..."

Idiotic questions which incorporate deception and flat self-contradiction in order to flummox other people so that we can laugh at them are not 'beautiful.' They are the opposite.
posted by koeselitz at 8:22 AM on October 30, 2011

Koeselitz, I feel bad for having been rude, since it became clear that he wasn't trolling after all, but are you suggesting we take the earlier any-statement-has-a-fifty-fifty-chance-of-being-correct-because-correct-and-incorrect-form-a-binary-opposition comments as having been intended as merely a description of the crazy, anything goes world created by this simple oscillating paradox on a chalkboard? That's not really borne out by the context.

But I think we agree that the original chalkboard question is just a silly game. I disagree, however, about its purpose being mockery. Would you say the same thing about the standard liar's paradox? They resolve down to the same sort of oscillation between contradictions (though, as pointed out above, this one would be cleaner if 0% were one of the listed options).
posted by nobody at 8:34 AM on October 30, 2011

And since I'm here, let me put in another plug for the self-referential aptitude test that jocelmeow linked to above. I'm glad I found the time to puzzle through it (pen and paper are a must, trial & error guessing is completely unnecessary) and maybe it'll satisfy your requirements for beauty. Thanks for posting that, jocelmeow!

(And I might as well point out -- after all the word-question interpretation wrangling going on in this thread -- that when a question there refers to answers, for example, being vowels, it is referring only to the A through E choices, ignoring the "answers" that those letter choices represent.)

(perhaps it's also solvable with the other interpretation -- in which case it would be pretty amazing -- but I solved it as described above)
posted by nobody at 8:45 AM on October 30, 2011

koeselitz: Babblesort was absolutely right.

Huh? About which part? Was he right that in the random experiment of drawing a card from a standard 52-card deck that the probability the card you pick is a diamond is 1/2?
posted by King Bee at 8:52 AM on October 30, 2011

He didn't say that, King Bee. He was right that this "statistics" question assumes binary probabilities that would make the chances of drawing a diamond 1/2. That is why the question is flatly absurd.
posted by koeselitz at 12:31 PM on October 30, 2011

if it were, it would take place in a weird world where correct and incorrect are statistically binary. That is: if this annoying and obnoxious question were at all valid, then it would make sense to say that everything has a fifty-fifty chance of either happening or not happening. But it doesn't.

I don't understand why you think this. Can you explain?
posted by painquale at 12:37 PM on October 30, 2011

(that is: I don't understand why you think the question assumes every statement has a fifty-percent chance of being correct.)
posted by painquale at 12:39 PM on October 30, 2011

I don't think it's that the question assumes every statement has a 50/50 chance of correctness, but that the idea of correct/incorrect is one-or-the-other, like being dead or alive is binary. You map that onto some scale where the scale represents the state of being dead or alive, not the likelihood of whatever animate (or previously animate) thing is IN that state. But maybe I'm completely missing something here. I can see it both ways, depending on whether we're mapping the conditions themselves, or some other thing that could be in one of the two conditions.
posted by iamkimiam at 2:51 PM on October 30, 2011

I don't think it's that the question assumes every statement has a 50/50 chance of correctness, but that the idea of correct/incorrect is one-or-the-other, like being dead or alive is binary.

But the phrase "50/50" does not mean binary. Not at all. It means that there is a 50 times out of a hundred chance that one thing will happen, and that 50 times out of a hundred another thing will happen. It does not simply mean "one thing or another." Those are completely different concepts.
posted by Sticherbeast at 4:11 PM on October 30, 2011

Yeah, I see that too. But what if you wanted to map that? (Not saying it's a sensible thing to do, but if you did it anyway, you'd choose something like 50/50, 37/37 or 0/100...basically something that is same/same or nothing/all, right?)

Regardless, I'm going to stop talking out my ass here and re-read the thread instead. I'm clearly taking too much of the literal/nerd-view while demonstrating my lack of understanding of the terminology, which is embarrassing.
posted by iamkimiam at 4:22 PM on October 30, 2011

I don't think it's that the question assumes every statement has a 50/50 chance of correctness, but that the idea of correct/incorrect is one-or-the-other, like being dead or alive is binary.

I don't think this is what koeselitz meant, but koeselitz didn't explain very much, so it's hard to say. Koeselitz did intend to defend Babblesort though, and Babblesort was certainly making a different claim than this.
posted by painquale at 4:39 PM on October 30, 2011

To wit: one of the stupid things about this question (one among many) is that it is not a statistics question at all.

Well I was wondering this, probably for different reasons, to wit (again): the question on the chalkboard does not claim to be a statistics question - which does not mean to say it is not a statistics question, just that it does not make a positive claim to be so - and it is only labeled a statistics question by the blog that reported it.
posted by carter at 5:35 PM on October 30, 2011

I'd also be interested in hearing more from koeselitz about why Babblesort isn't confused.
posted by Kwine at 9:18 PM on October 30, 2011 [1 favorite]

Damn it damn it DAMN it! I got most of the way through the Self-Referential Aptitude Test, I only had something like three questions left, which would have gone quickly and I would have been fine and felt all proud of myself when I suddenly remembered the answer. From elementary school. (Yes, I did this problem in elementary school. I had a pretty cool class in fifth grade.)

How depressing.

Another thing to note, in case anyone happens by this thread later and could use this information: that page will at times mark answers wrong when they are not. It still had one struck through and red under the "SOLVED" stamp. So, regrettably, it's not trustworthy in that way. Go pen-and=paper.
posted by Because at 2:59 PM on October 31, 2011

This sentence is true.

Is the previous sentence true or false?
posted by flabdablet at 9:06 PM on November 3, 2011

Either one! (and thus maybe we can call it a meaningless anti-paradox?)
posted by nobody at 2:24 AM on November 6, 2011

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