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Topic: Easy: COIN UNBIASING (Read 13334 times) |
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towr
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Re: Easy: COIN UNBIASING
« Reply #25 on: Oct 1st, 2009, 3:53am » |
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on Oct 1st, 2009, 3:27am, singh_sukhu wrote:i think i have made some calculation errors...
Any ways I hope my idea is clear... |
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The first one is; the second not so much. For one thing, you say "values of m and k may be so chosen according to given p such that A=p/q", but there is no guarantee such m and k can be chosen as integers as would be required.
But I'm not really clear on the rest either. In step 1, the number of heads/tails follows a binomial distribution; I see nothing that takes this into account later on.
Maybe you could give an example of how the process works? For, say, p=3, q=7 ?
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nakli
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Re: Easy: COIN UNBIASING
« Reply #26 on: Oct 1st, 2009, 8:27am » |
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Yes. I made that mistake . I noticed it later.
I'd rather have to work on them equations.
However the idea was that probability changes in 'three doors problem'. Can some similar logic be used here...??
Meanwhile google churned out something to chew upon..
http://www.eecs.umich.edu/~qstout/abs/AnnProb84.html
PLUS my method of the first part just requires one toss! 
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Benny
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Re: Easy: COIN UNBIASING
« Reply #27 on: Oct 7th, 2009, 1:38pm » |
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I wonder if you flip a coin n times and you get n-1 Tails, and on the n-th trial Heads, what are the chances that your coin is unfair?
Adding a background to Von Neumann simple method : Flip the coin twice. If it comes up heads followed by tails, then call the outcome HEAD. If it comes up tails followed by heads, then call the outcome TAIL.
Persi Diaconis' Dynamical Bias in the Coin Toss
And,
The author uncovers bias in a flip of a coin
The author says, flipped coins tend to come up the same way they started ... For natural flips, the chance of coming up as started is about .51 .... a flipped coin is more likely than not (51%) to come up the same way it started.
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nakli
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Re: Easy: COIN UNBIASING
« Reply #28 on: Oct 7th, 2009, 11:52pm » |
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on Oct 7th, 2009, 1:38pm, BenVitale wrote:
The author uncovers bias in a flip of a coin
The author says, flipped coins tend to come up the same way they started ... For natural flips, the chance of coming up as started is about .51 .... a flipped coin is more likely than not (51%) to come up the same way it started.
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This conclusion was reached after studying merely '25' tosses. Isn't the number too less?!!
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nakli
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Re: Easy: COIN UNBIASING
« Reply #29 on: Oct 7th, 2009, 11:57pm » |
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on Oct 7th, 2009, 1:38pm, BenVitale wrote:I wonder if you flip a coin n times and you get n-1 Tails, and on the n-th trial Heads, what are the chances that your coin is unfair?
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No matter how many tosses with a given coin we do , and study the outcomes, the outcomes alone can never prove that the coin is biased or unbiased.
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towr
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Re: Easy: COIN UNBIASING
« Reply #30 on: Oct 8th, 2009, 12:41am » |
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on Oct 7th, 2009, 11:52pm, singh_sukhu wrote:| This conclusion was reached after studying merely '25' tosses. Isn't the number too less?!! |
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Considering that one coin flip accounts for 4%, yes. You can't even get 51% of one outcome.
on Oct 7th, 2009, 11:57pm, singh_sukhu wrote:| No matter how many tosses with a given coin we do , and study the outcomes, the outcomes alone can never prove that the coin is biased or unbiased. |
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It can give overwhelming support to the hypothesis though. It is extremely unlikely to get predominantly one side of a coin turning up in a fair coin.
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Pyotr
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Re: Easy: COIN UNBIASING
« Reply #31 on: Jan 24th, 2011, 9:31am » |
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on Jul 27th, 2002, 11:11am, srowen wrote:Another decent solution:
1) Flip the coin twice.
2) If you get HT, guy #1 wins. If you get TH, guy #2 wins. These are equally probably, regardless of p.
3) If you get HH or TT, go to step 1). |
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Another possibility would be to have the condition that both players must always call either Heads or Tails.
They must both bet on the same side of the coin.
Would that work?
For biasing an unbiased coin, one could simply multiply one player's result by a factor that gave them the needed handicap. This is not as elegant as the binary digit solution, of course, as it doesn't set a limit for the number of throws needed for a fair result, but it should get the job done.
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