Mathslive.ie

PROBABILITY

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