3 ms·

> the question I am asking is whether it is possible to always get heads, an infinite number of times No. By my definition (lay, may be wrong), the probabilit

by paol 10y ago

> the question I am asking is whether it is possible to always get heads, an infinite number of times No. By my definition (lay, may be wrong), the probability is the ratio of heads to tails to which we converge at the limit (infinity). The only way for it to converge to 0 is if the probability of heads was 0 to begin with, which would contradict the initial assertion that it was a fair coin. By the way, from your previous comment it seems to me that you're struggling with getting an intuitive grasp on arguments that rely on infinity. To most people (me included for sure) it's initially difficult to accept that infinity is qualitatively different than a finite amount. Our brain seems to superficially accept the concept, but really it keeps trying to reason about it as a really large (but still finite) quantity. Are you familiar with the argument of whether 0.999... equals 1? (Spoiler: it does) Some people have a really hard time coming to terms with it, and the fundamental problem for many comes down to the same difficulty of reasoning about infinity. Also, it's a fun way to troll people :)

danbruc 10y ago
No. By my definition (lay, may be wrong), the probability is the ratio of heads to tails to which we converge at the limit (infinity). The only way for it to converge to 0 is if the probability of heads was 0 to begin with, which would contradict the initial assertion that it was a fair coin. This seems problematic to me. You can not perform an infinite number of coin tosses and know to what the relative frequency converges. So how do you conclude that a fair coin has probability of 0.5 for heads then? I can't really put my finger on it, but that argument is somehow circular. The probability is what the relative frequency converges to and I can not get anything other than 0.5 because that means to probability would have to have been not 0.5 to begin with. I can really only say that I disagree, I just can't pin it down exactly. Are you familiar with the argument of whether 0.999... equals 1? (Spoiler: it does) Some people have a really hard time coming to terms with it, and the fundamental problem for many comes down to the same difficulty of reasoning about infinity. I am aware of that and it seems totally obvious to me. And I also certainly know that infinity is not just a really huge number, but I am not sure I internalized that well enough to not make any mistakes because of the difference. Actually I am pretty sure I make mistakes because of that.

by paol 10y ago

danbruc 10y ago

No. By my definition (lay, may be wrong), the probability is the ratio of heads to tails to which we converge at the limit (infinity). The only way for it to converge to 0 is if the probability of heads was 0 to begin with, which would contradict the initial assertion that it was a fair coin. This seems problematic to me. You can not perform an infinite number of coin tosses and know to what the relative frequency converges. So how do you conclude that a fair coin has probability of 0.5 for heads then? I can't really put my finger on it, but that argument is somehow circular. The probability is what the relative frequency converges to and I can not get anything other than 0.5 because that means to probability would have to have been not 0.5 to begin with. I can really only say that I disagree, I just can't pin it down exactly. Are you familiar with the argument of whether 0.999... equals 1? (Spoiler: it does) Some people have a really hard time coming to terms with it, and the fundamental problem for many comes down to the same difficulty of reasoning about infinity. I am aware of that and it seems totally obvious to me. And I also certainly know that infinity is not just a really huge number, but I am not sure I internalized that well enough to not make any mistakes because of the difference. Actually I am pretty sure I make mistakes because of that.