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Trying to understand the basic idea behind probability: If you have a dice, and you throw it an infinite number of times, then the probability of getting each side of the dice is 1/6. So far logical. Now, this predicate "infinite number of times" is what disturbs me. Is the science of probability all based on this unrealistic assumption?

If we were to transform the problem to that of life and death. What is a probability that a person will die in the next second? Answer is 1/2 : either yes, either no. What if the person has an incurable disease, what is the probability of the person to die in the next second? Answer is still 1/2 : either yes, either no. OR Answer is 1 / (estimated quantity of remaining time to live?). Because simply there is no way to repeat the experiment an infinite number of times, both persons have equal probability of living!!

Excuse me for this weird question,thanks you very much for your time!

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    The probability of getting one particular side on a **fair** die *in a single throw* is $1/6$ (among other things because that's the *definition* of "fair die"); you don't need to "throw it an infinite number of times." But if you *actually throw* a die, say, 600 times, you will probably not get exactly 100 times an outcome of 1, exactly 100 outcomes of 2, etc. Instead, there will be a small variation between the expected probability (1/6 for each side) and the actual observed outcomes. What you expect is that discrepancy to diminish as the number of rolls increases.2011-10-31
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    Thanks. OK, so there is an assumption of 'fairness', and the number of experiment has to reach a meaningful threshold. These two predicates are essential!2011-10-31
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    I certainly hope the probability of my dying in the next second is a lot less than $1/2$. The mere fact that there are two possible outcomes does not make them equally likely. There are real philosophical difficulties in speaking of probabilities of events that are not repeatable. See http://en.wikipedia.org/wiki/Probability_interpretations2011-10-31
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    @k.honsali: No: the "assumption of fairness" is just that there are dice that are *loaded*; you don't expect those dice to behave the same as regular dice. (Do you expect a two-headed coin to fall heads half the time, and tails the other half?) As to "number of experiments has to reach a meaningful threshold"... a "meaningful threshold" for **what**? Not for probability to work. That's not it at all. You seem to be confusing a specific observations with probability. If you toss a coin and it falls heads, then it's been heads 100% of the time. Does that disprove the theory of probability?2011-10-31
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    @k.honsali: Your second paragraph is also incorrect. Just because there are two possible outcomes does not mean each outcome is equally likely. Is there life on Mars? 50% probability yes, 50% probability no. Is there *intelligent* life on Mars? 50% probabilty yes, 50% probability no? That would mean that you have the same probability of having life and of having intelligent life, which is certainly not the case.2011-10-31
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    In simple terms: two possible outcomes does not mean a 50% chance of occurrence each, as one may be more probable than the other (namely in dying / not-dying each second); flipping neither heads nor tails will preclude you from continuing to flip the coin, while dying will be the end of the dying / not-dying question, so you have a false analogy on your hands.2011-10-31
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    @A. Magidin: Thanks a lot! "If you toss a coin and it falls heads, then it's been heads 100% of the time" has opened my eyes on the observation/probability paradigm. Also, equality of probability in the Marsian example.2011-10-31
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    @R. Israel: Thanks.2011-10-31

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