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  • $\begingroup$ In your first main paragraph you seem to have confused $\alpha$ and $1-\alpha$. Where does the value of 10^12+1 come in? What do you mean by "beheaded"?? This text looks like it is need of proofreading and revision. $\endgroup$ Commented Jan 19, 2011 at 18:30
  • $\begingroup$ $10^{12}$ is for the trillion fair coins, and 1 is for the unfair coin. And I haven't confused $\alpha$ and $1-\alpha$ the Clopper Pearson interval listed [here][1] $\endgroup$ Commented Jan 20, 2011 at 2:43
  • $\begingroup$ [sorry typo] $10^{12}$ (TeX fixed) is for the trillion fair coins, and 1 is for the unfair coin, one over this is a rough approx. to the probability of having the "bad" coin. Beheaded is the consequence of giving the wrong confidence interval. And I haven't confused $\alpha$ and $1-\alpha$ the Clopper Pearson interval listed on the wiki page (search binomial proportion confidence interval). What happens is one part of the C-P interval is a tautology $1 \geq \frac{\alpha}{2}$ when one 1 observation. The side "flips" when X=1 to X=0, which is why there is $1-\theta$ and $\theta$. $\endgroup$ Commented Jan 20, 2011 at 2:52
  • $\begingroup$ Do you mean @Keith Winstein's answer? $\endgroup$ Commented Jan 20, 2011 at 23:00
  • $\begingroup$ @whuber, yes I do mean keith winstein's answer. $\endgroup$ Commented Jan 21, 2011 at 5:39