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%

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If you say no, Elwood and I will come here for breakfast, lunch, and dinner every day of the week.

It depends.

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The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Question X:If you choose an answer to Question X at random, what is the chance you will be correct?

Please first define Question X.

To make things more desperate you should extend this to ...


(A) 20% (B) 50% (C) 60% (D) 20% (E) 0%

EdLee, the question refers to itself. So, "this question" is the question you read.

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If you say no, Elwood and I will come here for breakfast, lunch, and dinner every day of the week.

Zero. Without further information we can only assume that all answers are possible. Therefore the choices form a finite subset of an infinite number of possible answers. The density is zero.

If, on the other hand, all possible correct answers are listed and each is considered equally likely then the probability is one third.

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Still officially AGA 5d but I play so irregularly these days that I am probably only 3d or 4d over the board (but hopefully still 5d in terms of knowledge, theory and the ability to contribute).

Measure or (in some cases, depending on the use) capacity is zero. A set does not have density, but is either dense or not (depending on a metric.)

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Geek of all trades, master of none: the motto for my blog mostlymaths.net

Agreed. But most people here are not mathematicians. As I was writing in English I used a term which I would expect to be clearer to everyone.

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Still officially AGA 5d but I play so irregularly these days that I am probably only 3d or 4d over the board (but hopefully still 5d in terms of knowledge, theory and the ability to contribute).

Got it, I just read it in mathematician eyes but now I think of it I can't find a clearer English word aside from density. Weird, I bet there should be one...

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Geek of all trades, master of none: the motto for my blog mostlymaths.net

Since it may be any random distribution with any probability, there are an infinite number of such probabilities but only a finite number of available answer probabilities. Hence the answer is: "almost 0". With a model of an increasing number of distributions and finally infinitely many, the answer is: "converges to 0 from its positive side".

I'm reminded of the mathematician joke that ends with the punchline, "The mathematician picks up the flamethrower and sets the house on fire, thereby reducing the problem to a case previously solved."

In English "to choose at random" means to choose so that each option has the same probability of being chosen.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

%0.0 Chance given that the correct answer is not actually listed.

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Thinking like a go player during a game of chess is like bringing a knife to a gun-fight. Thinking like a chess player during a game of go feels like getting knifed while you're holding a gun...

I'd say that "to choose at random uniformly / with a uniform distribution" would mean this. At least in (precise) German, one needs to say "gleichverteilt zufällig wählen".

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The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

So you believe the statement, "He played at random", indicates that the 1-1 points were as likely to be chosen as Tengen? I believe that English in the hands, hmmm... in the mouths that is, of us normal folks has nothing like the precision that can be ascribed to mathematical jargon.

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Dave Sigaty
"Short-lived are both the praiser and the praised, and rememberer and the remembered..."
- Marcus Aurelius; Meditations, VIII 21

What is the correct answer to this question?
(A) Answer B is correct.
(B) Answer A is correct.

They are both correct. If A is the correct answer then it says that B is the correct answer, which is fact true. And vice versa.

Alternatively, neither are correct. If A is wrong then it says B is not the correct answer, so A is wrong. And vice versa.

Take your pick.

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Still officially AGA 5d but I play so irregularly these days that I am probably only 3d or 4d over the board (but hopefully still 5d in terms of knowledge, theory and the ability to contribute).

(A) Statement B is true.
(B) Statement A is false.