Bill Spight wrote:In English "to choose at random" means to choose so that each option has the same probability of being chosen.
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".
Deutlich ist Deutschlich.
The Adkins Principle: At some point, doesn't thinking have to go on?
— Winona Adkins
RobertJasiek wrote: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".
In English "to choose at random" means to choose so that each option has the same probability of being chosen.
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.
Dave Sigaty
"Short-lived are both the praiser and the praised, and rememberer and the remembered..."
- Marcus Aurelius; Meditations, VIII 21
mitsun wrote: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.
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).
RobertJasiek wrote: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".
In English "to choose at random" means to choose so that each option has the same probability of being chosen.
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.
From Merriam-Webster's Dictionary:
One sense: "being or relating to a set or to an element of a set each of whose elements has equal probability of occurrence <a random sample>; also : characterized by procedures designed to obtain such sets or elements <random sampling>"
Another sense: "lacking a definite plan, purpose, or pattern"
The first sense is the one for choosing among given alternatives at random. The second is the one for playing at random.
The Adkins Principle: At some point, doesn't thinking have to go on?
— Winona Adkins
One sense: "being or relating to a set or to an element of a set each of whose elements has equal probability of occurrence <a random sample>; also : characterized by procedures designed to obtain such sets or elements <random sampling>"
Another sense: "lacking a definite plan, purpose, or pattern"
The first sense is the one for choosing among given alternatives at random. The second is the one for playing at random.
Exactly! The first sense is what professionals in the field do. The second sense encapsulates my entire life in seven words!
Dave Sigaty
"Short-lived are both the praiser and the praised, and rememberer and the remembered..."
- Marcus Aurelius; Meditations, VIII 21
entropi wrote: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%
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.
The fact that this is formulated as a multiple choice question implies that "choose an answer" intends to mean "choose one of (A),(B),(C), or (D)".
How do you come up with one third?
If you say no, Elwood and I will come here for breakfast, lunch, and dinner every day of the week.
entropi wrote: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%
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.
The fact that this is formulated as a multiple choice question implies that "choose an answer" intends to mean "choose one of (A),(B),(C), or (D)".
How do you come up with one third?
There are three possible values to choose. If it is random that means one in three.
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).
