I vastly prefer Bayes Theorem as ratios vs. percentages (plug, wrote about it here: http://betterexplained.com/articles/understanding-bayes-theorem-with-ratios/

I vastly prefer Bayes Theorem as ratios vs. percentages (plug, wrote about it here: http://betterexplained.com/articles/understanding-bayes-theorem-with-ratios/ http://betterexplained.com/articles/understanding-bayes-theo...) I like a "factor label" style approach where you can see the prior probability (Fair: Biased), the information about the flips, and the posterior probability (the revised chances after the new information is taken into account): Prior * Information = Posterior so (Fair : Biased) * (10 Fair heads : Fair ) : (10 Biased heads : Biased) = 10 Fair Heads : 10 Biased Heads Plugging in, we'd have: (999 / 1) * (1 / 1024 ) / (1 / 1) = 999 / 1024 The odds are ever-slightly in favor of a biased coin. So we can mentally guess ever-slightly above 3/4 for the chance of another heads. We could write (999/2 + 1024) / (999 + 1024) on the whiteboard to be exact.