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**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%**

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,846

Hmmm, looks like a paradox.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,613

Oh that's a great one! It seems to me that this is caused by the self referential nature of the question. It's a bit like the question "Am I lying now?"

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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Agnishom wrote:

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%

I would want to change this to:

**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%**

Even better

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**barbie19022002****Member**- Registered: 2013-05-24
- Posts: 1,314

maybe 50% because I am very good at guessing but at times it maybe 0% too...I am not sure..

Why is T called island letter?

think, think, think and don't get up with a solution...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,846

That made it much easier to calculate. According to Weakipedia it is all of the above.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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Maybe because it is **Weak**ipedia?

Bobbym, do you think that #4 makes the paradox more stronger ruling out none of the above?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**SteveB****Member**- Registered: 2013-03-07
- Posts: 577

It is possible to have an UNSOUND multiple choice rather than simply one that could be had to have "a non 100% percent chance

of you being considered correct by an infinitely* intelligent (imagined) person". (* = impossible in practice)

I have encountered this concept before, but for obvious reasons I shall not give a real example.

However I could easily make up a deliberately flawed multiple choice question about a factual subject:

What is the capital of France:

(1) Red

(2) Blue

(3) Purple

(4) Orange

Well none of them because all of those are colours, and we wanted a town for strarters, and we know that Paris is correct.

(Maybe there is a very very small chance that one could be argued to be correct due to a highly eccentric pseudo-course,

but if it were an ordinary thing like an exam then it would be an accidental error and considered unsound.

Bad for an exam because no student could ever be certain of getting the answer right about a matter of fact,

but on the other hand perhaps a strange history course might have said that a colour were the answer at some

point in history. Obviously this is NOT true, but if it were then it might be possible if that insight were both known and true.)

The question is not simply difficult, but impossible, because none of the choices is a satisfactory answer.

I would say that although you have created a very clever and amusing brain teaser in mathematics my answer would be:

Just like the above answer, although there is a paradox in yours and no paradox in mine, your question is a deliberately

unsound multiple choice in which is very possible that if you were to take a survey and work out a rough estimate of the

number of people that give the answers shown you could very easily get no answer at all being correct.

On the other hand: I suppose it could be that by an amazing coincidence one of them IS in fact correct fundamentally,

in which I may have to work upon my own definitions to make that better because otherwise a rare exception might

give a valid answer, but you would have to be Mystic Meg* to know what the answer would be.

(Not allowed for a hypothetical exam, but in terms of a brain teaser the questioner has a "licence" to think creatively.)

* = Replace with any fortune teller name of person thought of as able to predict the future precisely.

Mystic Meg is often used informally in the UK to refer to an imagined person able to predict the future to be able to

say "I'm not Mystic Meg" instead of "I am not a magician" and so on in appreciation of an astrologer with this psuedonym.

(Some of my questions are unsound by accident to be fair. None of us are right always.)

*Last edited by SteveB (2013-07-10 05:36:33)*

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

SteveB wrote:

Mystic Meg

Over here we often use the name "baba Vanga", who was a real person, though.

*Last edited by anonimnystefy (2013-07-10 05:53:23)*

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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SteveB, did you read post 4? If you say that all of them are wrong, then it is 0%, so you may not say that either

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**SteveB****Member**- Registered: 2013-03-07
- Posts: 577

Agnishom wrote:

SteveB, did you read post 4? If you say that all of them are wrong, then it is 0%, so you may not say that either

Yes that was a good touch, because it creates a recursive problem where first 0% appears a good answer, then because it

could be argued to be correct then becomes wrong.

I sometimes resort to statistical answer at this point like "25% on the grounds of there being four answers", but you have

predicted that answer by making 25% two choices rather than one !! Obviously not possible for an exam question, but

if you have a creative licence then the questioner can do this as a brain teaser, joke or something.

(It reminds me of deadlock and livelock in Computer Science.

From memory many years ago I think that deadlock was more than one process queued "waiting for each other" in some way.

I think that livelock was supposed to mean an indefinite wait which is either rather too long, or held up for ever if made

an accidentally infinite wait. Those two defintions may not be strictly correct because I cannot remember the full details.)

I did think of another statistical way to define the answer based upon "a survey of the entire population" to give meaning to

the probability of getting the answer right, but it is personalised to the reader by the fact that it is whether "I" can get the

answer right or not. The answer to that is therefore not dependent upon the population (also there are about 7 billion of them

I doubt if all of them will be able to read, some may be born at any time etc etc etc. so of course you cannot ever literally

survey the entire planet or universe obviously).

Okay then can I survey myself. So do I have to answer the question an infinite number of times and give a precise answer

depending upon whether I am right or not in each case, and who do I ask to determine whether I am right? I cannot even

be sure whether I am right in ONE case let alone an indefinite number (infinity etc.) so I could estimate the probability

according to a hideous arbitrary function....

It also reminds me of "the set of all sets" which is defined to be not an allowable set because apart from being way too

big even for the number "infinite" to really sum the thing up if it contains the set containing all subsets including the

set itself then since it contains ALL things it must already contain sets that it could not have contained initially.

I don't think I can explain that one properly without looking up the reason given usually, but it would not be difficult

to make up a proof by contradiction that the set of all sets does not equal itself and therefore is not a well defined set.

I suppose you could perhaps if you created a "foundations of mathematics" style structure for an acceptable multiple

choice question reject your multiple choice on the grounds that the correct answer does not equal itself.:)

I think a paradox is when two true things appear to contradict each other.

What is even more funny is that if you did want to put this in a maths exam you would probably have to nest the multiple

choice bit within a question making clear that an answer was not enough, and that full marks would only be given for a

full answer not just literally "abracadabra: the answer is .... ".

Multiple choice has it's place in an exam, but imagine if they nest a multiple choice within another, testing the person

spotting the paradox and then choosing the correct reason why the thing is a paradox. That would be a good one.

*Last edited by SteveB (2013-07-10 07:01:52)*

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**SteveB****Member**- Registered: 2013-03-07
- Posts: 577

Okay here goes my attempt at a strange nested multiple choice question:

(I may have to work on this one a bit because this is rather improvised.)

If this is a multiple choice question:

(

If this is a multiple question:

What is the probability of a correct answer to this

(1) 25%

(2) 0%

(3) 25%

(4) 50%

)

What is the correct reason:

(1) None of the available options are 100%

(2) It is a recursive paradox

(3) It is impossible, but 0% is an answer

(4) 25% is mentioned twice ambiguously

(5) 50% is also mentioned in case you are arguing that since 25% is there twice the answer is 50% this is also there so is 100% correct if this is your argument. 33.3 recurring is omitted.

(6) All of those

(7) The probability of this question being sound is not very high

(8) The probability of this question being answered right is not great

(9) Sorry that one was a comment not an option.

)

For the above how likely are you to get the answer to the outer bit right as a percentage?

I might have to work on that. Face it if you have chosen an answer then you have decided that it is 100% correct. You are therefore right and also wrong.

They should have that as an entrance question for something.

I always thought that mathematicians told the best jokes. That was a bad question on a number of levels.

*Last edited by SteveB (2013-07-10 07:40:44)*

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

Agnishom wrote:

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%

One more answer could be "it depends on how we choose, i.e. what the distribution of the random choice is".

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,846

Hi;

Bobbym, do you think that #4 makes the paradox more stronger ruling out none of the above?

I think the first question was okay, although I had different reasons for why it has no answer.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**mathaholic****Member**- From: Earth
- Registered: 2012-11-29
- Posts: 3,246

c

Mathaholic | 10th most active poster | Maker of the 350,000th post | Person | rrr's classmate

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julianthemath wrote:

c

Explain

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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