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marsh8472
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 Flipping heads forever   « on: Feb 6th, 2015, 8:07pm » Quote Modify

Say I start flipping a coin forever.  Sooner or later I would be expected to get 2 heads in a row, and 3 heads in a row, and 4 heads in a row etc...

Would it be correct to say that eventually a point would be reached where we would just flip heads forever?

The same could be said of flipping tails forever but it would be impossible to flip heads forever and tails forever at the same time.  I don't know where I'm going with this but feel free to comment.
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towr
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 Re: Flipping heads forever   « Reply #1 on: Feb 7th, 2015, 2:36am » Quote Modify

The probability that, from some point onward, you flip any particular sequence forever is 0.
However, the you could flip a particular sequence until you die (or otherwise stop) with a non-zero probability.
If you flip coins forever, any particular finite sequence should occur infinitely often. But not every infinite sequence (i.e. from now on forever) would occur infinitely often, or even be probable.

I think the probability of having a particular infinite sequence from now on is the same as some day having that infinite sequence from then on, i.e. 0.
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marsh8472
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 Re: Flipping heads forever   « Reply #2 on: Feb 7th, 2015, 7:06am » Quote Modify

It's like if I pick a random point on a circle what is the probability of picking point A?  Since there are infinite points it would be 0.  But at the same time, no matter what point is picked it would have had a probability of 0 also.

Technically it wouldn't be 0  it's just lim n-> infinitey 1/(2^n) = 0.  But if I flipped a coin forever the probability that I would end up flipping whatever sequence I end up flipping would be 0 by the same logic.
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rmsgrey
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 Re: Flipping heads forever   « Reply #3 on: Feb 8th, 2015, 8:18am » Quote Modify

on Feb 7th, 2015, 7:06am, marsh8472 wrote:
 It's like if I pick a random point on a circle what is the probability of picking point A?  Since there are infinite points it would be 0.  But at the same time, no matter what point is picked it would have had a probability of 0 also.   Technically it wouldn't be 0  it's just lim n-> infinitey 1/(2^n) = 0.  But if I flipped a coin forever the probability that I would end up flipping whatever sequence I end up flipping would be 0 by the same logic.

You have to be a little careful about what you mean by probability here.

Depending on your views on determinism, before you start flipping, the probability of getting the exact sequence you end up getting could be 1, or could tend to 0 in the limit as the number of flips increases. After you've flipped the coin that many times, the probability of having got the sequences you actually did get is 1.

The probability of 0 may be better thought of as the chance of flipping the exact same sequence if you flipped the coin an infinite number of times again. It happened, but there's no chance of doing it again...
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