Math Formulas

Basics
Probability of an Event :
$ P(A) =\dfrac{\text{m}}{\text{n}} $

where, m = Number of possible +ve outcomes

and n = total number of possible outcomes

Range of Probability Values :
$0 ≤ P(A) ≤ 1 $
Certain Event :
$P(A) =1 $
Imposible Event :
$P(A) =0 $
Complement :
$P(\overline {A}) = 1 - P(A) $
General Addition Rule :
$ P(A~ \cup~ B)$ $=P(A)$ $+~ P(B) $ $-~ P(A~ \cap~ B)$
Independent Event :
  • $P(A) = P(A~|~B)$
  • $P(B) = P(B~|~A)$
  • $P(A~ \cup~ B) =P(A) + P(B)$
  • $P(A~ \cap~ B) =P(A) \cdot P(B)$
Conditional Probability :
  • $P(A~ |~ B) =\dfrac{P(A~ \cap~ B) }{P(B)}$
  • $P(A~ \cap~ B) =P(B) \cdot P(A~|~B)$ $=P(B) \cdot P(B~|~A)$
Baye's Theorem :
$P(A~ | ~B)= \dfrac{P(A) ~ P(B~|~A)}{P(B)}$