# Multiple choice conundrum

**URL:** <https://boards.straightdope.com/t/multiple-choice-conundrum/978611>\
**Category:** Factual Questions\
**Created:** [January 22, 2023, 3:47pm UTC](https://boards.straightdope.com/t/multiple-choice-conundrum/978611 "2023-01-22T15:47:48Z")\
**Posts on this page:** 11\
**Page:** 1

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**Author:** ![Czarcasm](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/czarcasm/32/4050_2.png) [@Czarcasm](https://boards.straightdope.com/u/Czarcasm)\
**Post date:** [January 22, 2023, 3:47pm UTC](https://boards.straightdope.com/t/multiple-choice-conundrum/978611/1 "2023-01-22T15:47:48Z")

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I saw this elsewhere:  
If you pick an answer to this question at random, what is the chance that you are correct?  
A) 25%  
B) 50%  
C} 60%  
D) 25%

No, there are no misprints. 😄  
I’m thinking the answer is “B”. Am I right?

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**Author:** ![colinfred](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/colinfred/32/21338_2.png) [@colinfred](https://boards.straightdope.com/u/colinfred)\
**Post date:** [January 22, 2023, 3:52pm UTC](https://boards.straightdope.com/t/multiple-choice-conundrum/978611/2 "2023-01-22T15:52:24Z")

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No good answers. You have a 50% chance of picking 25% and a 25% of picking 50% so neither are correct.

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**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\
**Post date:** [January 22, 2023, 4:18pm UTC](https://boards.straightdope.com/t/multiple-choice-conundrum/978611/3 "2023-01-22T16:18:03Z")

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For one thing, it depends on whether “correct” means you have to match the letter or the answer that the letter stands for.

But this has been discussed before:

> [@Probability question -](https://boards.straightdope.com/t/probability-question/950030):
>
> I just saw this online: If you choose an answer to this question at random, what is the chance that you will be correct? A. 25% B. 0% C. 50% D. 25%

> [@Anyone want to try to solve this riddle?](https://boards.straightdope.com/t/anyone-want-to-try-to-solve-this-riddle/601335):
>
> If you choose an answer to this question at random, what is the chance you will be correct? A) 25% B) 50% C) 0% D) 25%

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**Author:** ![Themenin0](https://avatars.discourse-cdn.com/v4/letter/t/a183cd/32.png) [@Themenin0](https://boards.straightdope.com/u/Themenin0)\
**Post date:** [January 22, 2023, 4:23pm UTC](https://boards.straightdope.com/t/multiple-choice-conundrum/978611/4 "2023-01-22T16:23:09Z")

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It might need a closer parsing, but at first blush there’s no question to answer.

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**Author:** ![Riemann](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/riemann/32/3133_2.png) [@Riemann](https://boards.straightdope.com/u/Riemann)\
**Post date:** [January 22, 2023, 4:23pm UTC](https://boards.straightdope.com/t/multiple-choice-conundrum/978611/5 "2023-01-22T16:23:50Z")

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Isn’t it just a reframing of

> All SDMB posters are liars

> **[Epimenides paradox](https://en.wikipedia.org/wiki/Epimenides_paradox)**
>
> The Epimenides paradox reveals a problem with self-reference in logic. It is named after the Cretan philosopher Epimenides of Knossos (alive circa 600 BC) who is credited with the original statement. A typical description of the problem is given in the book Gödel, Escher, Bach, by Douglas Hofstadter:
> Epimenides was a Cretan who made the immortal statement: "All Cretans are liars."\[a\] A paradox of self-reference arises when one considers whether it is possible for Epimenides to have spoken the ...

It’s just that you must do a little more work to figure out the inherent self-contradiction.

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**Author:** ![The\_Other\_Waldo\_Pepper](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/the_other_waldo_pepper/32/12370_2.png) [@The\_Other\_Waldo\_Pepper](https://boards.straightdope.com/u/The_Other_Waldo_Pepper)\
**Post date:** [January 22, 2023, 4:26pm UTC](https://boards.straightdope.com/t/multiple-choice-conundrum/978611/6 "2023-01-22T16:26:01Z")

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> [@Riemann](#):
>
> Isn’t it just a reframing of
> 
> > All SDMB posters are liars

> [@](#):
>
> It’s just that you must do a little more work to figure out the inherent self-contradiction.

How is that one a contradiction?

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**Author:** ![thorny\_locust](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thorny_locust/32/431_2.png) [@thorny\_locust](https://boards.straightdope.com/u/thorny_locust)\
**Post date:** [January 22, 2023, 7:02pm UTC](https://boards.straightdope.com/t/multiple-choice-conundrum/978611/7 "2023-01-22T19:02:34Z")

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> [@Themenin0](#):
>
> t might need a closer parsing, but at first blush there’s no question to answer

That’s my reaction: my chances are effectively zero, because there’s no way to tell what the question is.

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**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\
**Post date:** [January 22, 2023, 7:15pm UTC](https://boards.straightdope.com/t/multiple-choice-conundrum/978611/8 "2023-01-22T19:15:16Z")

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> [@thorny\_locust](#):
>
> there’s no way to tell what the question is.

The question is “If you pick an answer to this question at random, what is the chance that you are correct?”

It’s self-referential, and possibly paradoxical or ill-defined, but it is a question.

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**Author:** ![thorny\_locust](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thorny_locust/32/431_2.png) [@thorny\_locust](https://boards.straightdope.com/u/thorny_locust)\
**Post date:** [January 22, 2023, 7:17pm UTC](https://boards.straightdope.com/t/multiple-choice-conundrum/978611/9 "2023-01-22T19:17:14Z")

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But it appears that the field of answers one’s choosing from is all the answers in the universe. Because there’s nothing there that says “all the possible answers are listed below.”

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**Author:** ![Riemann](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/riemann/32/3133_2.png) [@Riemann](https://boards.straightdope.com/u/Riemann)\
**Post date:** [January 22, 2023, 7:36pm UTC](https://boards.straightdope.com/t/multiple-choice-conundrum/978611/10 "2023-01-22T19:36:21Z")

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> [@thorny\_locust](#):
>
> Because there’s nothing there that says “all the possible answers are listed below.”

I think that’s implicit in the multiple choice format.

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**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\
**Post date:** [January 22, 2023, 7:45pm UTC](https://boards.straightdope.com/t/multiple-choice-conundrum/978611/11 "2023-01-22T19:45:13Z")

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Your chance of getting the right answer is 0%. And 0% isn’t one of the options, so you have 0% chance of picking it.
