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Which answer in this list is the correct answer to this question? (2017)

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Re: Which answer in this list is the correct answer to this question? (2017)

#41

Post by cyborgx7 »

AstralStorm wrote: post #32
cyborgx7 wrote: post #29

Earlier quoted context omitted.

>0% and 100% are indefensible for any uninformed prior. If none of the answers are correct, the chance of picking the correct answer is 0%.

Again, not for a question that has a defensible answer present when you're picking at random. (Uninformed prior.) If there is no defensible answer present, it's still not 0%, it's a paradox. The answer is dependent on base axioms accepted. (Axiom of choice and axiom of regularity are a few.) The answer set is Dedekind-finite and countable, whereupon probability is 1/logically consistent answers given the axioms chose…

Of course, a uniform distribution is implied. The fact that you choose to misunderstand this on purpose, doesn't make you smart or right. It makes you a pedant who is still wrong.

Re: Which answer in this list is the correct answer to this question? (2017)

#42

Post by olalonde »

AstralStorm wrote: post #25
cyborgx7 wrote: post #19

Earlier quoted context omitted.

The answer to that question is obviously 0% Now, what would be the answer to the same question with the answer options: A) 20% B) 40% C) 60% D) 20% E) 0%

Your answer above is incorrect in a very funny way. "At random" implies an uninformed prior, but the question presupposes there's a correct answer, as 0% is missing. 0% and 100% are indefensible for any uninformed prior. There are two answers giving the correct probability for uniform prior. One of the 25% is a wrong answer despite being indistinguishable. Such a thing can happen because of a typo or in any myriad of…

> One of the 25% is a wrong answer despite being indistinguishable. Such a thing can happen because of a typo or in any myriad of ways. It's not a paradox.

Sorry but that seems disingenuous... You are ready to accept that there's a mistake in one of the answers but not that none of the answers are correct?

Re: Which answer in this list is the correct answer to this question? (2017)

#43

Post by lovasoa »

Here is a single python statement that solves the problem:

    print([
        q for q in itertools.product((True, False), repeat=6)
        if q == (
            all(q[1:]),  # 1. All of the below.
            not any(q[2:]),  # 2. None of the below.
            all(q[:2]),  # 3. All of the above.
            any(q[:3]),  # 4. One of the above.
            not any(q[:4]),  # 5. None of the above.
            not any(q[:5]),  # 6. None of the above.
        )
    ])
https://gist.github.com/lovasoa/f2b4ed93e755bf4172583d28f206...

Re: Which answer in this list is the correct answer to this question? (2017)

#44

Post by nyhc99 »

dtjohnnyb wrote: post #17

Similar one I enjoyed in the Naive Bayes article from yesterday https://blog.floydhub.com/naive-bayes-for-machine-learning/ Multiple Choice: If you choose an answer to this question at random, what is the chance you will be correct? A) 25% B) 50% C) 60% D) 25%

So this one is an actual paradox, right?

If they would accept both correct answers, then the answer would be 50%, but then if it's 50% those two correct answers would be incorrect.

Re: Which answer in this list is the correct answer to this question? (2017)

#45

Post by vagab0nd »

I feel the question is unnecessarily convoluted. To really answer the question, you have to recursively refer to the question itself. So to parse the question, I'm calling a function recursively without a stop condition. They could have just asked, which statement below is true. And for all intents and purposes the answer would have been the same.

Re: Which answer in this list is the correct answer to this question? (2017)

#47

Post by gowld »

mazsa wrote: post #12

Only the 5th is true, Metamath: $( THEOREM=noneabove LOC_AFTER=? h50::noneabove.1 |- ( ph ( ( ps /\ ch /\ th ) /\ ( ta /\ et ) ) ) h51::noneabove.2 |- ( ps ( -. ch /\ ( -. th /\ -. ta ) /\ -. et ) ) h52::noneabove.3 |- ( ch ( ph /\ ps ) ) h53::noneabove.4 |- ( th ( ph \/ ps \/ ch ) ) h54::noneabove.5 |- ( ta ( ( -. ph /\ -. ps /\ -. ch ) /\ -. th ) ) h55::noneabove.6 |- ( et ( ( -. ph /\ -. ps /\ -. ch ) /\ ( -. th /…

Is this readable with more linebreaks?

Re: Which answer in this list is the correct answer to this question? (2017)

#48

Post by thegeekpirate »

lovasoa wrote: post #43

Here is a single python statement that solves the problem: print([ q for q in itertools.product((True, False), repeat=6) if q == ( all(q[1:]), # 1. All of the below. not any(q[2:]), # 2. None of the below. all(q[:2]), # 3. All of the above. any(q[:3]), # 4. One of the above. not any(q[:4]), # 5. None of the above. not any(q[:5]), # 6. None of the above. ) ]) https://gist.github.com/lovasoa/f2b4ed93e755bf4172583d28f20…

Run it online here: https://onlinegdb.com/rkZhWVniH

Re: Which answer in this list is the correct answer to this question? (2017)

#49

Post by decasia »

thaumasiotes wrote: post #20
PeterStuer wrote: post #9

6 can not be true because if it where then 1,2,3,4 & 5 would be false, but that would make 5 true as well which is a contradiction, therefore 6 can only be false 1 Can not be true because we just determined 6 as false so 1 can only be false 3 can not be true because we just determined 1 as false so 3 can only be false With 1 and 3 now proven false, 2 can only be true if 4 is false, but if 2 is true then 4 would be tr…

Everyone in the comment thread seems to be focused on whether each proposition can be true. This is looking for your keys under the lamppost despite the fact that you dropped them in the dark. It's easy to determine whether a proposition can be true. But the question doesn't ask about that. It just asks "which of these is the correct answer to this question?" There are no stated criteria for being the correct answer,…

This seems like a crucial problem with the initial question. As with so many puzzles like this, it assumes that the reader will make similar (unargued, unstated) assumptions as the writer.

But what justifies that methodological assumption? Nothing, as thaumasiotes is pointing out.

Re: Which answer in this list is the correct answer to this question? (2017)

#50

Post by mazsa »

gowld wrote: post #47
mazsa wrote: post #12

Only the 5th is true, Metamath: $( THEOREM=noneabove LOC_AFTER=? h50::noneabove.1 |- ( ph ( ( ps /\ ch /\ th ) /\ ( ta /\ et ) ) ) h51::noneabove.2 |- ( ps ( -. ch /\ ( -. th /\ -. ta ) /\ -. et ) ) h52::noneabove.3 |- ( ch ( ph /\ ps ) ) h53::noneabove.4 |- ( th ( ph \/ ps \/ ch ) ) h54::noneabove.5 |- ( ta ( ( -. ph /\ -. ps /\ -. ch ) /\ -. th ) ) h55::noneabove.6 |- ( et ( ( -. ph /\ -. ps /\ -. ch ) /\ ( -. th /…

Is this readable with more linebreaks?

Not editable anymore but here you are (cf. http://us.metamath.org/metamath/set.mm ) :

h50::noneabove.1 |- ( ph ( ( ps /\ ch /\ th ) /\ ( ta /\ et ) ) )

h51::noneabove.2 |- ( ps ( -. ch /\ ( -. th /\ -. ta ) /\ -. et ) )

h52::noneabove.3 |- ( ch ( ph /\ ps ) )

h53::noneabove.4 |- ( th ( ph \/ ps \/ ch ) )

h54::noneabove.5 |- ( ta ( ( -. ph /\ -. ps /\ -. ch ) /\ -. th ) )

h55::noneabove.6 |- ( et ( ( -. ph /\ -. ps /\ -. ch ) /\ ( -. th /\ -. ta ) ) )

56:50:simprbi |- ( ph -> ( ta /\ et ) )

57:56:simprd |- ( ph -> et )

58:51:simp3bi |- ( ps -> -. et )

59:57,58:anim12i |- ( ( ph /\ ps ) -> ( et /\ -. et ) )

60::pm3.24 |- -. ( et /\ -. et )

61:60,59:mto |- -. ( ph /\ ps )

62:61,52:mtbir |- -. ch

63:50:simplbi |- ( ph -> ( ps /\ ch /\ th ) )

64:63:simp2d |- ( ph -> ch )

65:62,64:mto |- -. ph

66::3ioran |- ( -. ( ph \/ ps \/ ch ) ( -. ph /\ -. ps /\ -. ch ) )

67:53:notbii |- ( -. th -. ( ph \/ ps \/ ch ) )

68:67,66:bitri |- ( -. th ( -. ph /\ -. ps /\ -. ch ) )

69:68:anbi1i |- ( ( -. th /\ -. th ) ( ( -. ph /\ -. ps /\ -. ch ) /\ -. th ) )

70::pm4.24 |- ( -. th ( -. th /\ -. th ) )

71:69,70,54:3bitr4i |- ( -. th ta )

72::nbbn |- ( ( -. th ta ) -. ( th ta ) )

73:71,72:mpbi |- -. ( th ta )

74::df-xor |- ( ( th \/_ ta ) -. ( th ta ) )

75:73,74:mpbir |- ( th \/_ ta )

76::xoror |- ( ( th \/_ ta ) -> ( th \/ ta ) )

77:75,76:ax-mp |- ( th \/ ta )

78:55:simprbi |- ( et -> ( -. th /\ -. ta ) )

79::pm4.56 |- ( ( -. th /\ -. ta ) -. ( th \/ ta ) )

80:78,79:sylib |- ( et -> -. ( th \/ ta ) )

81:77,80:mt2 |- -. et

82:51:simp2bi |- ( ps -> ( -. th /\ -. ta ) )

83::pm4.56 |- ( ( -. th /\ -. ta ) -. ( th \/ ta ) )

84:82,83:sylib |- ( ps -> -. ( th \/ ta ) )

85:77,84:mt2 |- -. ps

86:65,85,62:3pm3.2ni |- -. ( ph \/ ps \/ ch )

87:86,53:mtbir |- -. th

88:87,75:mtpxor |- ta

89:65,85,62:3pm3.2i |- ( -. ph /\ -. ps /\ -. ch )

90:89,87:pm3.2i |- ( ( -. ph /\ -. ps /\ -. ch ) /\ -. th )

qed:90,88,81:3pm3.2i |- ( ( ( -. ph /\ -. ps /\ -. ch ) /\ -. th ) /\ ta /\ -. et )

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