[Closed] Probability/Multiple Choice

However, I still keep getting drawn back to 1 in 3

If the answer is one of the unique answers - 1 in 4 chance of getting it right

If the answer is one of the duplicated answers - 1 in 2 chance of getting it right

Seeing as we have both these possibilities, lets go with somewhere in between the two and with no mathematical justification, say 1 in 3 🙂

Or have I totally missed the point here?

yes.

if it was
a) blue
b) yellow
c) red
d) blue
then it wouldn't be a paradox.

If the answer is one of the unique answers - 1 in 4 chance of getting it right

If the answer is one of the duplicated answers - 1 in 2 chance of getting it right

exactly - you can't pick the correct answer.
it's a vicious circularity paradox.

But if you consider each answer in turn, it is wrong. So the probability is zero since you cannot pick a right answer (which is the wording of the original question.

In that case - 50%. You either pick the right, or the wrong answer.

*finds nearest doorway to put head in* anyone want to repeatedly close the door really hard?

If the answer is 25% then you have a 50% chance of picking it, if the answer is 50% then you have a 25% chance of picking it so I'm going with 0

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%

Thinking about this a bit more, I'm starting to wonder if this is a null question, as in the same frame as:

What hippo makes yellow sky?

1. Yes
2. Memory
3. 128 (and a bit)
4.

It just makes no sense. So you choose an answer at random, then ask yourself are you correct? Correct about what? There is no question to be correct about, as the only question is asking what the probability if of being correct, but there's nothing to be correct about in the first place, so you get stuck in a loop that has no start.

UNLESS, you consider the question to be hidden and unstated, and that one of the answers is correct. But then as you've got two 25%s, the answer is 0%, even though it's not an answer (like I said before).

Whichever, it's annoying because 'correct' is basically a meaningless term in the original question although phil.w is probably right if it's supposed to be a paradox, but I still think that depends on 25% being the correct answer.

The question is 'what is the chance of you being correct'

The answer is 0% which isn't one of the choices. So it's equivalent to asking

What is 2+2?

a) 5
b) 6
c) 7
d) 8

... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%, no... 25%, no... 50%....

Idiots.

The answer and the answers are related.

So you are answering the question regarding the chance of being right, using the answers that you are randomly choosing from.

There's no point trying to analyse it - it's a circular argument.

Statistically the answer is impossible to identify as we do not know what the question is that has generated those four choices - but, for the light of brain amongst you, you've decided that the four answers in some way direct the possibility of random correctness.

The probability of being correct is between 0 and 1.

Here endeth the lesson.

DrRS****
BSc Applied Statistics

Does that mean I can stop now?

So you listened to him but not me?

Yeah, he's a Dr and he's got letters after his name.

TBH, I thought my answers made it clear I knew it was a paradox from the outset.

I know, just messin wit ya.

Depending on how you interpret the question, it's either,

a) I'm right,
b) It's a paradox,
c) It's a nonsense question made up in about 5 seconds by someone who doesn't actually have an answer to it, in order to waste the time of people who think they're clever.

Who's for "c"? I've not actually found a definitive source or answer for this and am starting to think there isn't one.

Statistically - Answer C is correct Cougar.

There is no answer.

We have been presented with a question and a set of answers - but the two are not related.

TSY - never stop 😉

It's easy to make up questions that don't have an answer, and it's REALLY easy to make up multiple choice ones that don't.

This one is sort of fun because it's self referential which adds a bit of a twist, but it's fundamentally no different to asking "What is the sun's favourite cheese?"

...gorgonzola, no... edam, no...gorgonzola, no... edam, no...gorgonzola, no... edam, no...gorgonzola, no... edam, no...gorgonzola, no... edam, no...gorgonzola, no... edam, no...gorgonzola, no... edam, no...gorgonzola, no... edam, no...gorgonzola, no... edam, no...gorgonzola, no... edam, no...gorgonzola, no... edam, no...gorgonzola, no... edam, no...gorgonzola, no... edam, no...gorgonzola, no... edam, no...gorgonzola, no... edam, no...gorgonzola, no... edam, no...gorgonzola, no... edam, no...gorgonzola, no... edam, no...gorgonzola, no... edam, no...gorgonzola, no... edam, no...gorgonzola, no... edam, no...gorgonzola, no... edam, no...gorgonzola, no... edam...

I've just emailed it on and got a response of

25% chance of choosing 50%. As there are 2 25% then the answer is b) 50%.

I'm not sure I understand what that means! This could be fun

Four possible answers means a 25% chance of getting it right, seeing as two of the answers are 25% you have a 50% chance of picking one of them, but there's only one answer of 50% so you have a 25% chance of picking it, and seeing as two of the answers are 25% you have a 50% chance of picking one of them, but there's only one answer of 50% so you have a 25% chance of picking it, and seeing as two of the answers are 25% you have a 50% chance of picking one of them, but there's only one answer of 50% so you have a 25% chance of picking it, and seeing as two of the answers are 25% you have a 50% chance of picking one of them....

I've just emailed it on and got a response of

25% chance of choosing 50%. As there are 2 25% then the answer is b) 50%.

The answer is 0% you tards, which isn't one of the options.

**** me is this one still going.

As a former mathematician I would say that the correct answer can be anything between 0% (if none of the answers are correct) and 50% (if the correct answer is 25% or whatever the one is that is repeated)..

On the basis of two key assumptions, that are

1/ One of the answers is in fact correct
2/ They are all equally likely to be correct

Then the answer is 33%. QED.

Not sure where DrRS**** get's his answer 0-100% from. I think he may have jumped to that without any real thought -poor form for a statistician 😆

By your thinking molgrips, then there is no answer, as 0% isn't an option.

That's what I've been saying all thread. No answer - unanswerable question.

I've had time to think about this now that I'm not in work. What do we think of this:

The probability of you choosing any one of the answers is 1 in 4, that's 25%, or 0.25.

Assuming that one of the answers [i]is[/i] correct (otherwise it's a nonsensical trick question), the probability of a) being correct is 0.5, of b) being correct 0.25, c) 0.25, d) 0.5.

So. The probability of you guessing a) and a) being correct is 0.25 x 0.5, or 0.125. The probability of guessing b) and being correct is 0.25 x 025 = 0.0625. Of c), 0.0625, and of d), 0.125.

So, the probability of you choosing the right answer is the total of those four probabilities. 0.125 + 0.0625 + 0.0625 + 0.125 = 0.375.

If you choose an answer to this question at random, what is the chance you will be correct? You will be correct 37.5% of the time.

I think.

Wow, some of the reasoning employed here actually gave me a headache.

Speaking as a member of the IOP*, this is as previously noted a restating of Russell's paradox:

"if R is the set of all sets which do not contain themselves, does R contain itself?"

Incidentally, this forms an example of Goedel's incompleteness theorem, which was part of the reason that Russell gave up on maths and became a philosopher.

* I am not now, nor have I ever been a member of the IOP

Cougar your problem is that you are double counting - your probabilities of a, b, and d add up to 1.5. Probability can only be between 0 and 1. You have double counted your a) and d)

What do we think of this

that your thinking about it too much 🙂

it's an unanswerable question as the answer is 25% until you give the answer then it becomes 50% until you give the answer then it goes back to 25% and so on....

it's got bugger all to do with statistics and any other forms of mathematics. it is a variation of a vicious circle paradox.

it's a slightly more complex version of this one... (not really more complex, the maths element just makes it miss leading)

"this sentence is false"
or
"is the answer to this question no?"

both of which lead you into a never ending circle where the answer changes as soon as you give the answer.