The probability of every sequence will be zero. Even the subset of all sequences in which |H-T|<2 will be of measure zero. So if you actually want an operational test you need to define some range (0.5-e, 0.5+e) you will consider "fair". Then you can define a test have specified probabilities of alpha/beta errors. Brent On 3/4/2016 9:00 PM, Dan Asimov wrote:
Not *exactly* true. A fair coin can have any sequence in {H, T}^omega show up. The probability is often 0, but that doesn't keep something from happening.
—Dan
On Mar 4, 2016, at 6:48 PM, Eugene Salamin via math-fun <math-fun@mailman.xmission.com> wrote:
True, but not useful if one can only perform finitely many tosses.
-- Gene
From: Tom Karzes <karzes@sonic.net> To: math-fun <math-fun@mailman.xmission.com> Sent: Friday, March 4, 2016 6:28 PM Subject: Re: [math-fun] how to test whether a coin is fair
Assuming a fixed probability per toss, with each toss independent of each other toss, I believe The Law of Large Numbers says that h/(h+t) must converge to the true probability of the coin landing on "heads".
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