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Coin Flipping 4 Years, 1 Month ago
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This is a math problem I just thought of. If I were to take a balanced toin (heads on one side tails on another) and flip it over and over an infinite number of times. Is it possible to get heads for eternity?
My intuition says yes at first. But mathematically...
probability of not getting tails for an eternity is lim x->infinity (1/2)^x = 0
And the probability of getting tails at least once can be represented as 1/2 + 1/4 + 1/8 + 1/16 + ... which by definition is 1. Kind of like those 0.99999... = 1 problems
Yet there is no finite amount of flips where it is imossible to not get all heads and at any given flip it is possible to get heads. So I don't know.
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Re: Coin Flipping 4 Years, 1 Month ago
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[quote1207724374=Marshall]
This is a math problem I just thought of. If I were to take a balanced toin (heads on one side tails on another) and flip it over and over an infinite number of times. Is it possible to get heads for eternity?
My intuition says yes at first. But mathematically...
probability of not getting tails for an eternity is lim x->infinity (1/2)^x = 0
And the probability of getting tails at least once can be represented as 1/2 + 1/4 + 1/8 + 1/16 + ... which by definition is 1. Kind of like those 0.99999... = 1 problems
Yet there is no finite amount of flips where it is imossible to not get all heads and at any given flip it is possible to get heads. So I don't know.
[/quote1207724374]
Each flip has an independent probability of 50% either way. So if you've gotten one side any number of times in a row, that has absolutely no effect on the probability of the next flip, no matter how many times you've flipped.
It seems like you're just subtly leaning towards the gambler's fallacy.
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The kind of philosophy one chooses depends upon what kind of person one is. ~ J.G. Fichte
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Re: Coin Flipping 4 Years, 1 Month ago
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It is actually not the gambler's fallacy if you look at the probability from the outset--before you start flipping. E.g., the probability of getting two heads in a row is 1/2 * 1/2 = 1/4. The prob. flipping 3 heads in a row is 1/2 * 1/2 * 1/2 = 1/8. But if you flip a coin and get heads twice the probability you will get heads the NEXT time (after already flipping twice) is still 1/2. It is a subtle distinction.
It is not possible to get a number of heads in a row infinitely. Your mathematical reasoning is correct. Infinity is a LONG time--it never ends, so you would be bound to get at least one head if you flip forever.
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Nec pluribus impar.
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Re: Coin Flipping 4 Years, 1 Month ago
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Karma: 1
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[quote1207761028=Michael132]
It is actually not the gambler's fallacy if you look at the probability from the outset--before you start flipping. E.g., the probability of getting two heads in a row is 1/2 * 1/2 = 1/4. The prob. flipping 3 heads in a row is 1/2 * 1/2 * 1/2 = 1/8. But if you flip a coin and get heads twice the probability you will get heads the NEXT time (after already flipping twice) is still 1/2. It is a subtle distinction.
It is not possible to get a number of heads in a row infinitely. Your mathematical reasoning is correct. Infinity is a LONG time--it never ends, so you would be bound to get at least one head if you flip forever.
[/quote1207761028]
I disagree.
I absolutely think that it IS possible to get heads ad infinitum, and the odds of it being heads is just 50% every time.
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The kind of philosophy one chooses depends upon what kind of person one is. ~ J.G. Fichte
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Re: Coin Flipping 4 Years, 1 Month ago
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at any given moment it's 50% since they're independent trials but to get heads infinity in a row should be 0. Or lim x-> infinity (1/2)^x.
I kind of knew the answer already I think. It's possible to get heads forever for any finite length of time but it's impossible to get heads an infinite number of times in a row. But when would you reach the event "an infinitity number of flips from now" Never. So it'll be impossible to get all heads up until the event that doesn't exist anyway.
So I think it's you can flip heads forever in theory but not an infinite number of times.
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Re: Coin Flipping 4 Years, 1 Month ago
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Karma: 1
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[quote1207766176=Marshall]
at any given moment it's 50% since they're independent trials but to get heads infinity in a row should be 0. Or lim x-> infinity (1/2)^x.
I kind of knew the answer already I think. It's possible to get heads forever for any finite length of time but it's impossible to get heads an infinite number of times in a row. But when would you reach the event "an infinitity number of flips from now" Never. So it'll be impossible to get all heads up until the event that doesn't exist anyway.
So I think it's you can flip heads forever in theory but not an infinite number of times.
[/quote1207766176]
I just don't see any reason why not.
Surely if there were always people, and they always flipped a coin, then there is a possible world in which a coin never came up tails even though each time for a never ending series of flips it has a 50% chance.
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