0
$\begingroup$

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!

  • 0
    @R. Israel: Thanks.2011-10-31

2 Answers 2

1

It's not based on that irrealistic assumption. The central limit theorem states just that you cover your intuition of probability of an event at infinity as an actual event: indeed, when talking about dice you have a complete knowledge about what is happening: you are assuming that the dice is non-loaded, so that any side has probability $\frac{1}{6}$. The central limit theorem tells you that you get that probability at infinity.

If you talk about life and death, you don't have any real way to estimate (non trivially) the probability to die the next second.

I think that the theory of probability is, from a philophical point of view, to give a certain value to an uncertain event, describing its quantity of uncertainty. But how can you do that if you don't know the quantity of uncertainty?

  • 0
    What does "extrapolate those results at infinity on the actual throw of dice" mean? And what does "safe" mean? If you mean, "can the gambler assume that on exactly $1$/6th of the throws he will get 1, on exactly 1/6th he will get 2, etc" then of course not (and it has nothing to do with the fact that 100 is not divisible by 6). What he *can* assume is that, on average, he can expect a particular outcome to occur *about* 1/6th of the time, with the "about" being closer and closer to exactly 1/6th the more throws he makes. That does not preclude "good/bad runs" from ocurring, though.2011-10-31
1

Part of your question has to do with the statisticians' debate over the frequentist vs. Bayesian interpretation of probability. This link here seems to have a fair explanation.

The second half of your question seems to make the mistaken assumption that, for all questions (such as will I die in the next second) the number of possibilities (2, yes or no) have equal probability. Clearly that's not true. There are two possibilities, but this is not a coin toss. Perhaps there are any number of freak accidents that could take me out in the next second, and I don't actually know if they're going to happen; so I have to give some probability to that eventuality, but the probability is quite small. This is the uncertainty/Bayesian interpretation. From a frequentist point of view, one could think of multiple time lines sprouting from the present reality--if those timelines represent all possible things that could happen (assuming that the future is actually occurring probabilistically, and not according to chaotic determinism), given the present circumstances, then perhaps, in some of those timelines, I die pre-maturely. But I sort of prefer the Bayesian interpretation in this case.

  • 0
    thanks @JCooper, I was just curious to push the limits of my understanding to a 'practical' implementation..2011-11-02