ece108: add bayes law 2

docs/1b/ece106.md

@@ -666,3 +666,5 @@ If there is a conducting loop in a time-varying magnetic field, a $V_{ind}$ is f
 $$V_{ind}=\oint\vec E\bullet\vec{d\ell}=-\frac{d}{dt}\int\vec B\bullet\vec{dS}$$
 
 Time-varying magnetic fields are formed if the field or charge is moving or if bounds change.
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+

docs/1b/ece108.md

@@ -927,3 +927,8 @@ $$\text{independent}\iff Pr\{A\cup B\}=Pr\{A\}+Pr\{B\}-Pr\{A\}Pr\{B\}$$
 **Bayes' theorem** provides a general formula for conditional probability:
 
 $$Pr\{A|B\}=\frac{Pr\{B|A\}}{Pr\{B\}}$$
+
+Formally, this can be solved without $Pr\{B\}$:
+
+$$Pr\{A|B\}=\frac{Pr\{A\}Pr\{B|A\}}{Pr\{A\}Pr\{B|A\}+Pr\{\overline A\}Pr\{B|\overline A\}}$$
+