Bayes-and-Certainty.md

@@ -26,6 +26,12 @@ The number of people who tested positive twice = 0.9 + 9.9 = 10.8
 
 Of these, the number of people who are actually sick: 9.9
 
-P = Number of sick people who tested positive twice / Number of tested positive twice = 9.9/(9.9 + 0.9) = 0.917
+P = Number of sick people who tested positive twice / Number of people who tested positive twice = 9.9/(9.9 + 0.9) = 0.917
 
-$P=a+b$
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+We can confirm that this is equivalent to the Bayes eqn as follows:
+
+9\.9/ 10.8 = 9.9 / (9.9 + 0.9) = 99(0.1)/((99(0.1) + 1(1-0.1)) = 100(0.99)(0.1) / ((100(0.99)(0.1) + (100 - 100(.99))(1-0.1)) =
+
+0\.99(0.1) / ((0.99(0.1) + (1-0.99)(1-0.1) )
+
+We recognize this result as the Bayes eqn.
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