[Closed] Probability/Multiple Choice

My brain started to smoke a bit after 20 seconds so Immagonna wait and join in later. 🙂

0%. But I hate probability. So could be wrong, but I don't think so.

1 in 3 chance

Assuming 25, 50 and 60 % are equally like to be correct then

(1/3 * 1/4) + (1/3)*(1/4) + 1/3*(1/2) = 1/12 + 1/12 + 1/6 = 4/12 = 33.333%

But surely you do not need the maths and it is obvious?

EDIT - few dodgy ( )

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

Either no one else has understood the question properly, or I'm thinking about this too deeply.

GJP - I got 33.3333........% (or 1 in 3) without any maths. There are three possible answers and you are picking one of them. Surely?

So, if you answer any four answer MC question at random, there's a one in four chance of getting it right i.e. 25%. But two of the answers are 25%. So is it now 50%?

I think the confusion (or twist/brain ****) is, is that the actual answer, isn't one of the answers.

It's impossible to choose an answer 'at random' surely.

RealMan = 0% isn't an option, so...

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

No darcy - if the actual answer is 25%, then you have a 50% chance. if it isn't, then you don't.

*edit* - that was my first approach anyway, but isn't correct

[i]*pulls up a chair*[/i]

ATSR - yes you are correct and that is the intuitive approach - I needed to derive it from first principles - you are probably a lot younger than me and my brain is ****ed

Although to my credit I actually stated the key assumption that all unique answers were equally likely to be correct whereas it was implicit within your intuitive thinking

RealMan = 0% isn't an option, so...

If you choose an answer at random, what is the probability you will be correct.

So you choose an answer, it won't be correct => probability = 0%.

Or something.

This statement is false, innit?

b)
50 % it is either right or wrong the number of choices is irrelevant I suspect the exact wording of the Q is critical to the answer.

There is no question

Surely there is no spoon...

Anyway, it's a paradox... of similar making to the one with the book that lists all books which don't reference themselves.

50 % it is either right or wrong the number of choices is irrelevant I suspect the exact wording of the Q is critical to the answer.

Yeah, you also have a 50% chance of winning the lottery, cause you can either win or lose, right?

Yes well spotted.

You cannot deny that each week i either win it or i dont there is no other chance. Obviously the odds/probabilities heavily favour one outcome but there are still only two chances hence 50%
I think the key is the word chance here and it is the semantics of the Q that is the issue here. It cannot be probability as others suggest as that would give 33% which is not an option.
Anyway I have more chance of being right than you as I went for an answer that was at least there 😛

It cannot be probability as others suggest as that would give 33% which is not an option.

So there is zero chance you'll be right?

So there is zero chance you'll be right?

There's two questions, with a similar set of answers, which is confusing. Compare,

If you choose an answer to this question at random, what is the chance you will be correct?
a) A
b) B
c) C
d) A

Answer, 33%.

Probably.

It's self referential, so it's a paradox and hence cannot be answered.

I'd be impressed if someone's come up with a new one though - there must be a recognised and named version of this problem surely? Game theory anyone? CharlieMungus to the forum, please.

So there is zero chance you'll be right?

that is some cruel mocking of my maths ability there grahamS 😥

Yes I should have realised its the opposite of what I think as this does seem to be the rule with any maths question on here

I did a bit of Googling.

I've seen suggestions that it's paradoxical and there is no answer, with "[url= http://en.wikipedia.org/wiki/Russell%27s_paradox#Informal_presentation ]Russell's Paradox[/url]" posited. Frankly that's beyond me, set theory to that degree makes me want to kill kittens.

I also found this analogy, which is ostensibly where I was going with it, only a bit better written:

There is a box containing two red balls, one blue ball, and one yellow ball. I secretly write down one of these colours on a piece of paper.

If you pick a random ball from the box, what is the probability that the ball is the colour written on the piece of paper?

Answer, 33%.

I'm convinced this is correct now, though the maths was breaking my head for a while.

Using the 'balls' analogy, cos it's easier; you pick a ball at random, what's the probability that it matches what's written on the paper? The key here is that [i]the contents of your ball bag doesn't matter(*).[/i] Whether you've got two red balls, a hundred red balls, or in fact only red balls, what are the chances of it matching a 1-in-3 random choice? It's 33%.

(*) - never thought I'd find myself typing that

Ooh, I think I've got it. Is the answer to this question no?

No.

I'm now questioning my own theory actually - if there are 100 red balls, one blue ball and one yellow ball, the chance of picking the yellow ball is 1 in 102.

Therefore if the answer is yellow (or blue), it's 1 in 102, whereas if the answer is red, you have a 100 in 102 chance?

Aaaaarrrgggghhhh!!!!!

Do I need to stand on a conveyor belt for this one?

Just for the record, anyone that thinks a plane on a conveyor belt would take off is a dumbass.

thankyou Cougar 🙂

it only took one post!

I want to win a goat. Which choice do I make for that?

A looong time since I was at school - can you add probabilities together like fractions, because if so, it revives the 1/3 theory

Red - 2/4
Yellow - 1/4
Blue - 1/4

Add together = 4/12 or 1/3

Works for 5 balls too, with 3 being red

Red - 3/5
Yellow - 1/5
Blue - 1/5

Add together = 5/15 or 1/3

Or is that just a load of nonsense?

I want to win a goat. Which choice do I make for that?

just don't switch doors when Monty give's the chance too.

Or is that just a load of nonsense?

It's nonsense. When adding fractions you don't add the denomenator, only the numerator.

Or is that just a load of nonsense?

It bears out my theory, so it's golden as far as I'm concerned. (Though as GF says, that's not how you add fractions, not that it matters)

Is it the fact that 2 of the numbers are the same rather than what the actual numbers are? There's nothing to say that any of them are 'correct'

So if the question is : if you choose one of 4 options at random and 1 of them is correct your chances are 1/4. If two of them are correct/the same (as the question sort of implies) then it's 2/4. If 2 are the same but incorrect then it's still 1/4.... is it?

Ha, yeah - of course. Stoopid me, I knew that anyway. Doh!

If you pick a random ball from the box, what is the probability that the ball is the colour written on the piece of paper?

Cougar that's not the same question.

In this case the correct ball depends on the ball you pick.. so it's a paradox.

s it the fact that 2 of the numbers are the same rather than what the actual numbers are?

it's both.

the two numbers the same change the probability of picking the correct answer from 25% to 50%. the correct answer becomse 50%. yet 50% is now not the correct answer as it only appears once thus making the correct answer 25% and so on...

[i]In this case the correct ball depends on the ball you pick[/i]

this.

is it the fact that 2 of the numbers are the same rather than what the actual numbers are?

it's both.

the two numbers the same change the probability of picking the correct answer from 25% to 50%. the correct answer becomse 50%. yet 50% is now not the correct answer as it only appears once thus making the correct answer 25% and so on...

Only if 25% is the correct answer to start with. Couldn't the question just as well say:

a) blue
b) yellow
c) red
d) blue

So the odds of the one you pick being the 'right' one depends on what the right one is, which we don't know? Or have I totally missed the point here?

EDIT: Someone's already said this haven't they?

No, you are probably right Mr Salmon

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.