Bayes-and-Certainty.md

+We've already discussed the fact that Bayes pulls in favor of certainty. If we combine a 99% opinion with a 10% opinion we get 91.7%. But if we increase the 99% to 99.9% the combined opinion rises to 99.1%. If we increase yet again to 99.99% the combined opinion rises to 99.91%. We summarize this below to make it easy to see:
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+99% combined with 10% ==\> 91.7%
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+99\.9% combined with 10% ==\> 99.1%
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+99\.99% combined with 10% ==\> 99.91%
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+See what's happening here? The combined opinion gets pulled very strongly toward the 1st opinion the more certain the first opinion becomes. It seems a little strange that what seems like small differences in the first opinion should have such a pronounced effect.
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+The Bayes eqn will confirm the truth of this but this situation begs for a more intuitive explanation. Although 99% and 99.9% don't seem like much of a difference, they represent a huge difference in sample sizes. To be able to say 99%, one must perform at least 100 experiments, 99 of which succeeded and 1 which failed. To be able to say 99.9%, one must perform at least 1000 experiments where 999 succeeded and 1 failed. And so on.
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