①BASICS
$P=\dfrac{\text{ways}}{\text{total}}$ · scale $0\to1$ · $P(\text{not }A)=1-P(A)$
②AND / OR
AND = × · OR = + · tree: multiply along, add between
③TWO DRAWS
Replaced → fractions same. Not replaced → total $-1$, colour $-1$. At least one $=1-P(\text{none})$
④VENN / OR
$P(A\text{ or }B)=P(A)+P(B)-P(A\cap B)$ · mutually exclusive $\Rightarrow$ empty overlap
⑤EXPECTED VALUE
$E(x)=\sum x\cdot P(x)$ · net $=E(x)-$ cost
⑥PERMUTATIONS
$n!$ arranges all $n$ · fill boxes & × · fussy box first · together $=$ bubble $\times$ inside