[Callan S.]

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%

I went through a few stages on this one, myself.

[MSJ]

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%

I went through a few stages on this one, myself.

50%, because A & D are obviously the same answer?

[Wilshire]

Other answers can be found if you google, but within the spoiler tags below is what I came up with before I did that .

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The chances of randomly selecting a correct answer to a question with 4 possible choices is 25%.

25% appears twice. so 2/4, or 50%.

The correct answer would then be B) 50%.

However, If the correct answer is B, your odds of choosing the correct answer is 1/4 (since 50% only appears 1 of 4 times), or 25%.

So the correct answer is A or D.

Making your random selection chances go back to 2/4 to be correct, or, again 50%.

So B.

But then...

etc.

---
So the answer changes the question, which means you can't solve it - ie there is no answer.
You could also say your chances are 0%, which  is not an available answer, so the correct answer does not appear, and the question is therefore unanswerable.

Thanks Callan

[Callan S.]

Wilshire, To be fair...

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The question asks what your chance of being correct are - it doesn't need to be an available choice for you to just auto fail the question. It's not unanswerable, just unwinnable! BTW, how long did it take you to figure it out? I came away with 50% at first but then hours latter while doing other stuff it clicked for me that that doesn't work out.

[Wilshire]

Wilshire, To be fair...

(click to show/hide)

The question asks what your chance of being correct are - it doesn't need to be an available choice for you to just auto fail the question. It's not unanswerable, just unwinnable! BTW, how long did it take you to figure it out? I came away with 50% at first but then hours latter while doing other stuff it clicked for me that that doesn't work out.

(click to show/hide)

Well I looked at it, decided the answer was 25%, then saw MSJ's answer and realized there was a bit more to it (its a riddle, duh). I was not particularly busy at work so I stared at it for 10 minutes thinking it through.  I wanted very badly to make one of the choices the correct answer, but couldnt do it .

[Hogman]

The question states that you should choose an answer at random. It doesn't state that each option should have an equal probability of being chosen. So you can make any of the options the correct answer by suitably defining the probability of each option being chosen. For example, I could make 60% the correct answer by assigning the  following probability distribution to my choice: (A) 40/3% (B) 40/3% (C) 60% (D) 40/3%. 

[Callan S.]

Pretty sure that's a dragon way of answering

IS NOT PROBABILITY INFINITE!?

[Callan S.]

Here's another

A bat and ball cost a dollar and ten cents. The bat costs a dollar more than the ball. How much does the ball cost?

Note: I find this one a bit bogus in how it uses a vague word for a non specific amount right next to a very specific amount. It's like saying 'there were a lot of sheep, 100 of them'.

[Somnambulist]

The ball costs 5 cents

[Hogman]

Here's another

A bat and ball cost a dollar and ten cents. The bat costs a dollar more than the ball. How much does the ball cost?

Note: I find this one a bit bogus in how it uses a vague word for a non specific amount right next to a very specific amount. It's like saying 'there were a lot of sheep, 100 of them'.

Which bit of this is vague?

[Callan S.]

'more'

Give some everyday uses of it before saying it's a specific word.

[Hogman]

Well, I make no claims about the word "more" being specific or vague because it depends on the context. "The bat costs more than the ball" is vague, but "the bat costs a dollar more than the ball" is specific.
Let me turn the question around: how would you rephrase it to make it more precise? I say it's impossible, because it's already as precise as it could be.

[Wilshire]

The question states that you should choose an answer at random. It doesn't state that each option should have an equal probability of being chosen. So you can make any of the options the correct answer by suitably defining the probability of each option being chosen. For example, I could make 60% the correct answer by assigning the  following probability distribution to my choice: (A) 40/3% (B) 40/3% (C) 60% (D) 40/3%. 

Yeah I saw this online, but I dont like it (and/or dont get it). Ignoring the choices themselves, it's implied that the probability is 25%. Randomly selecting one of  four answers is always 25% unless stated otherwise, because that's how probability works. Assigning whatever values you want doesn't make sense. Flipping a coin give you a 50-50 shot every time. Assigning heads a 75% chance to land up doesn't change the reality that its still 50%.

Well, I make no claims about the word "more" being specific or vague because it depends on the context. "The bat costs more than the ball" is vague, but "the bat costs a dollar more than the ball" is specific.
Let me turn the question around: how would you rephrase it to make it more precise? I say it's impossible, because it's already as precise as it could be.

Agreed. The only way to make it more specific would be to outright say how much the bat costs, but then there is no question.

Here's another

A bat and ball cost a dollar and ten cents. The bat costs a dollar more than the ball. How much does the ball cost?

Note: I find this one a bit bogus in how it uses a vague word for a non specific amount right next to a very specific amount. It's like saying 'there were a lot of sheep, 100 of them'.

Which bit of this is vague?

I think the trick is that if you read it quick maybe you are supposed to think the bat costs $1? So then you'd falsely assume the ball was 10c and get the answer wrong on the test?

[Hogman]

The question states that you should choose an answer at random. It doesn't state that each option should have an equal probability of being chosen. So you can make any of the options the correct answer by suitably defining the probability of each option being chosen. For example, I could make 60% the correct answer by assigning the  following probability distribution to my choice: (A) 40/3% (B) 40/3% (C) 60% (D) 40/3%. 

Yeah I saw this online, but I dont like it (and/or dont get it). Ignoring the choices themselves, it's implied that the probability is 25%. Randomly selecting one of four answers is always 25% unless stated otherwise, because that's how probability works. Assigning whatever values you want doesn't make sense. Flipping a coin give you a 50-50 shot every time. Assigning heads a 75% chance to land up doesn't change the reality that its still 50%.

I agree that one should assume each option has an equal probability unless stated otherwise, although I don't think "that's how probability works" is the best choice of words. I'd rather say "that's the convention". Often probability questions do make it explicit ("if a fair coin is tossed...", "if a fair die is rolled..." etc). In my opinion it's fair game to take advantage of a lack of explicitness in a "trick" question like this.

[Wilshire]

I'm not generally one for discussions about semantics (why am I here then...) but I get what your saying. I at least see where your coming from now.