diff --git a/docs/1b/ece108.md b/docs/1b/ece108.md index 779f4fd..868a5f3 100644 --- a/docs/1b/ece108.md +++ b/docs/1b/ece108.md @@ -911,3 +911,19 @@ $$Pr\{X^{-1}(\{x\})\}$$ Thus the **binomial distribution** for $r$ successes of $n$ total tries, if they are independent, is: $$Pr\{X=r\}{n\choose r}p^rq^{n-r}$$ + +### Independence + +Please see [SL Math - Analysis and Approaches 2#Conditional probability](/g11/mcv4u7/#conditional-probability) for more information. + +Two events are independent if they can be treated separately. + +$$\text{independent}\iff Pr\{A\cap B\}=Pr\{A\}Pr\{B\}$$ + +Or, via the inclusion-exclusion theorem: + +$$\text{independent}\iff Pr\{A\cup B\}=Pr\{A\}+Pr\{B\}-Pr\{A\}Pr\{B\}$$ + +**Bayes' theorem** provides a general formula for conditional probability: + +$$Pr\{A|B\}=\frac{Pr\{B|A\}}{Pr\{B\}}$$