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Is a coin toss fair?

We see countless probability problems dealing with 'biased coins'. I've also seen mentions that a biased coin is impossible (for coin flipping).

Is it impossible if weighting and small modifications in shape are allowed? The coin is being flipped.

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    Why should it be impossible? Could you please cite the source for this claim. Just apply some glue to one side and it is biased, and obvious but there are other more subtle ways.
    – Alexander
    Mar 4, 2012 at 15:04
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    Related: physics.stackexchange.com/q/9435/2451
    – Qmechanic
    Mar 4, 2012 at 15:05
  • @alexander :I don't know. I've seen it in the comments of various maths puzzle sites. Not exactly reliable, which is why I ask. Mar 4, 2012 at 15:24
  • I imagine if you bent the coin slightly in a vice it would make a noticeable difference to the probabilities. But really, the "biased coins" in probability questions are not meant to be actual coins, it's really more of a conceptual shorthand for any random process that has two possible outcomes, which might not be equally likely.
    – Nathaniel
    Mar 4, 2012 at 20:50
  • @Nathaniel Yes, I know about that. Mar 5, 2012 at 0:49

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