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#### grant

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« Reply #29 on: January 20, 2012, 08:41:30 PM »
There are 2 parts:
2) What chance do I have of randomly selecting it?

First the question:
25% would be the correct answer except it is represented twice, increasing your odds to 50%.
So I'd say the answer to the question is B (50% chance).

Now to the random part:
As 50% (B.) is the correct answer and only represented once out of 4 options, to randomly choose B. is a straight out one in four chance.

So you have a 25% chance of getting it right, so A. or D. are the correct answers.
What if the hokey pokey is what its all about?

#### Gnu Ordure

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« Reply #30 on: January 20, 2012, 09:46:55 PM »
^^^
Quote
So you have a 25% chance of getting it right, so A. or D. are the correct answers
And then go back to the question:
Quote
If you choose an answer to this question at random, what is the chance you will be correct?

If, as you say, the correct answers are A or D, and if you choose your answer at random, then your chance of getting a right answer is actually 50%. Therefore A or D are not the right answer, B is.

But if B is the right answer, there's only a 25% chance of getting that with a random throw, so it's not the right answer either. It must be A or D.

But if the correct answers are A or D, and if etc...

As kin hell pointed out, way back in post 10.
« Last Edit: January 20, 2012, 09:57:52 PM by Gnu Ordure »

#### Gnu Ordure

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« Reply #31 on: January 21, 2012, 12:07:06 PM »
Azdgari:
Quote
That is an identical question for the purposes of this problem.  The actual numerical values in the answers have not been shown to be relevant, other than the fact that two of them are the same.

But the values are relevant, in that we can set the question non-paradoxically so that there is a single correct answer, i.e.:

"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) 80%"

Do you agree that that question is self-referential but non-paradoxical? And that the correct answer is A?

So the values are relevant.

Setting D to 25% sets up a loop and makes the question unanswerable. (Or mu, as the Japanese say).

(There's another sort of paradox available if you consider adding option E) None of the above to the above question. If you add it, it becomes the right answer, because the chance of randomly choosing the right answer changes to 20%, which isn't offered).
« Last Edit: January 21, 2012, 12:14:15 PM by Gnu Ordure »

#### Azdgari

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« Reply #32 on: January 21, 2012, 12:37:12 PM »
That's the "other than" that I included in my post.
I always say what I mean. But sometimes I'm a sarcastic prick whose tone can't be properly communicated via text.

#### Gnu Ordure

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« Reply #33 on: January 21, 2012, 01:37:09 PM »
But having two of the options the same doesn't necessarily set up a loop. e.g:

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

A) 25%
B) 50% 60%
C) 60%
D) 80%

The probability of randomly selecting 60% as the correct answer is now 50%. 50=/=60, so it's still wrong, and A remains the only correct answer.

Whereas, duplicating the 50% does produce a contradiction:

A) 25%
B) 50%
C) 60% 50%
D) 80%

If the examiner has arbitrarily decided that 25 is the correct answer, then A is correct, because there is a 25% chance of randomly selecting it.

Whereas if he's arbitrarily decided that 50 is the right answer, B or C are correct, because there is a 50% chance of randomly selecting one of them.

So this version is invalid, because there are two possible solutions but no way of distingushing between them logically - only arbitrarily.

And of course the examiner can't accept both as correct, because then the new 'correct' answer would become 75%, and we would have another loop.

So the values are relevant.
« Last Edit: January 21, 2012, 01:41:57 PM by Gnu Ordure »

#### Azdgari

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« Reply #34 on: January 21, 2012, 02:00:47 PM »
Ahh.  I was assuming that the answer itself was unknown, and that the numbers were arbitrary and could be replaced with letters without a change.  Misunderstood the question.
I always say what I mean. But sometimes I'm a sarcastic prick whose tone can't be properly communicated via text.

#### kin hell

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« Reply #35 on: January 21, 2012, 04:05:17 PM »
Gnu
+1 mate for the extra quandaries
great work and great explanation
"...but on a lighter note, demons were driven from a pig today in Gloucester."  Bill Bailey

all edits are for spelling or grammar unless specified otherwise

#### Gnu Ordure

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« Reply #36 on: January 21, 2012, 04:21:01 PM »
Azd:
Quote
Misunderstood the question.
No worries. It was supposed to be confusing.

Quote
I was assuming that the answer itself was unknown
Since the question asks "the chance of being correct", the only possible right answers are 25%, 50%, 75%, or 100%, depending on how many times the correct answer is offered as an option. i.e. "25%" has to be offered once, "50%" twice, and so on. Anything else will produce a loop.

(Zero can't be as a correct answer, because it's the same as admitting that the question can't be answered. i.e. if zero is chosen as the correct answer, but not offered as an option, nobody can select it. But if zero is offered as an option, the chance of selecting it becomes 25%, i.e. no longer zero, which is another loop).

Good puzzle, though.

Gnu.
« Last Edit: January 21, 2012, 04:26:59 PM by Gnu Ordure »

#### Gnu Ordure

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« Reply #37 on: January 21, 2012, 04:45:56 PM »
Gnu
+1 mate for the extra quandaries
great work and great explanation
Thanks, kin. I'm only expanding on your post.

Are we right though?

We've had 5 or 6 people on this thread say that B is the right answer to the OP. A couple claimed 33.33%, one claimed "A or D", one suggested 37.5%.

My/our answer is "the question as posed sets up a self-referential paradox and can't be answered in its present form".

I'd still like to know who's right.
« Last Edit: January 21, 2012, 04:47:30 PM by Gnu Ordure »

#### kin hell

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« Reply #38 on: January 21, 2012, 04:53:36 PM »
Gnu
+1 mate for the extra quandaries
great work and great explanation
Thanks, kin. I'm only expanding on your post.

Are we right though?

We've had 5 or 6 people on this thread say that B is the right answer to the OP. A couple claimed 33.33%, one claimed "A or D", one suggested 37.5%.

My/our answer is "the question as posed sets up a self-referential paradox and can't be answered in its present form".

I'd still like to know who's right.

The whole purpose of the questions structure was obviously to create the paradox.

I will always hold my hands up and admit error if I am shown to be wrong, but in this case we are right.
"...but on a lighter note, demons were driven from a pig today in Gloucester."  Bill Bailey

all edits are for spelling or grammar unless specified otherwise

#### grant

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« Reply #39 on: January 21, 2012, 11:02:21 PM »
The question does not say to use A, B, C or D in the answer.

I believe the answer is "25%".

(Which is the chance of selecting B. out of the 4 options.)
What if the hokey pokey is what its all about?

#### Gnu Ordure

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« Reply #40 on: January 22, 2012, 03:49:21 PM »
Hi Grant,

You still have a loop there.

As you said,
Quote
There are 2 parts:
2) What chance do I have of randomly selecting it?
Right. So if the question-master arbitrarily selects a solution, let's say 25%, he can present four options in which "25%" is only offered once.

i.e. the answer is 25%, and the chance of selecting it is 25%. The two numbers are the same, so there is no loop and the question is valid, answerable by circling the appropriate letter.

For example, these sets of options...

A) 25%       I       A) 50%
B) 30%       I       B) 50%
C) 60%       I       C) 60%
D) 80%       I       D) 80%

... are both valid. In the first case, the question-master's answersheet says that 25% is the right answer, so A is correct. In the second, the question-master's answersheet says that 50% is the right answer, so A or B is correct.

In both cases, the percentage figure on the question-master's answersheet matches the percentage figure circled by the student - AND mathematically the probabilities are correct - in the first case, the chance of randomly selecting A)25% is 25%, and so on.

Quote
The question does not say to use A, B, C or D in the answer.
But that's how multiple-choice exams work. You circle the letter. That method works for the valid questions above.

Quote
I believe the answer is "25%". (Which is the chance of selecting B. out of the 4 options.)
In which case you can circle the appropriate letter, either A or D, which both say the answer is 25%.

And if you do so, your answer will be wrong, because you've decided that the question-master's answersheet says that B)50% is the right answer. As you said:
Quote
25% would be the correct answer except it is represented twice, increasing your odds to 50%.
So I'd say the answer to the question is B (50% chance).
So, if you think the answersheet says B, circling A or D will obviously be the wrong answer.

But B would also be wrong, because it is evident that the chance of choosing it randomly is 25%, not 50%, therefore the question-master's answer is mathematically wrong, and he has set an invalid problem.

I'm getting dizzy...
« Last Edit: January 22, 2012, 05:30:54 PM by Gnu Ordure »