Hi,Probably classical for some people, I ll post it thoughThree prisoners, A, B, and C have applied for parole. The parole board has decided to release two of the three, andthe prisoners know this but not which two. A warder friend of prisoner Aknows who are to be released. Prisoner A realizes that it would be unethical toask the warder if he, A, is to be released, but thinks of asking for the name ofone prisoner other than himself who is to be released He thinks that before heasks, his chances of release are 2/3. He thinks that if the warder says "B will bereleased," his own chances have now gone down to 1/2, because either A and Bor Band C are to be released. And so A decides not to reduce his chances byasking. However, A is mistaken in his calculations Explain.

QuoteProbably classical for some people...As in the coin-tossing problem, you don't seem to be clearly expressing what you probably mean. A problem is either classical or not. A problem's status as "classical" or otherwise doesn't depend on any individual reader. So presumably you mean "This is a classical problem. Therefore I expect that many readers are already familiar with it." Expressing yourself more analytically will help you in maths, whether brainteasers or otherwise, and is often a key to good quant performance.The problem is a version of the Monty Hall problem, and the underlying theory is known as "restricted choice". The false 50% argument is exactly the same false argument that says that switching or not switching is equally likely to get the car. 2/3 is the correct probability.CommodityQuant

The proba the other guy says B is 1/2.The proba the other guys says B and A is released is 1/3.So by Bayes Theorem the proba A is released knowing he says B is (1/3)/(1/2)=2/3.

QuoteA problem is either classical or not. A problem's status as "classical" or otherwise doesn't depend on any individual reader. How do problems get defined as classical?Is it because it stems from some branch of statistics formaly known as 'Classical Statistics'?Or because it was defined in the period known as Classical Antquity?Or something else entirely?

QuoteHow do problems get defined as classical?"Something else entirely" is the correct answer to your multiple-choice problem. It means, roughly speaking, that the problem is both well-known and considered to illustrate something important. For example, the Monty Hall problem is a classical illustration of restricted choice and therefore a classical problem.But I'm confused by your question. Your first two choices, "Classical Statistics" and "Classical Antiquity" are obviously ridiculous so I don't get what point you're trying to make."Classical" is an extremely common word among mathematicians and the OP was misusing it, and I pointed this out.It is possible that a more grammatical rendering might be "classic" instead of "classical" -- I don't know this. I used "classical" because that's what the OP said.CommodityQuant.

My question(s) are largely out of ignorance. I think 'classical' has a pretty wooly definition. For example, how well-known would a problem need to be before it becomes classical? How important does the something being illustrated need to be? Maybe it shoud be used with a confidence interval

QuoteOriginally posted by: MHillMy question(s) are largely out of ignorance. I think 'classical' has a pretty wooly definition. For example, how well-known would a problem need to be before it becomes classical? How important does the something being illustrated need to be? Maybe it shoud be used with a confidence interval Indeed! Whether something is "well known" is clearly a function of the individual reader. For most of the world's 7 billion people, nothing in probability and statistics is "classical".I count myself among those likely to know "classical problems" in math but had never seen this variant of the Monty Hall problem and initially thought this brainteaser was related to the classic game theory problem called "the prisoners dilemma".

CommodityQuant getting nervous again and raising philosophical questions about what "classical" means ... anyway, didn't expect this reaction/debate. Sounds like the problem has been clearly expressed, as you managed to find the right answer

QuoteOriginally posted by: Traden4AlphaQuoteOriginally posted by: MHillMy question(s) are largely out of ignorance. I think 'classical' has a pretty wooly definition. For example, how well-known would a problem need to be before it becomes classical? How important does the something being illustrated need to be? Maybe it shoud be used with a confidence interval Indeed! Whether something is "well known" is clearly a function of the individual reader. For most of the world's 7 billion people, nothing in probability and statistics is "classical".I count myself among those likely to know "classical problems" in math but had never seen this variant of the Monty Hall problem and initially thought this brainteaser was related to the classic game theory problem called "the prisoners dilemma".indeed, prisoner dilemma was the title of the thread .......