Probability Formula Sheet

Formula	Expression
Complement	P(A') = 1 - P(A)
Addition	P(A union B) = P(A) + P(B) - P(A intersect B)
Mutually exclusive	P(A union B) = P(A) + P(B)
Conditional	P(A\|B) = P(A intersect B) / P(B)
Multiplication	P(A intersect B) = P(A) * P(B\|A)
Independence	P(A intersect B) = P(A) * P(B)
Total Probability	P(A) = sum P(A\| $B_i$ ) * P( $B_i$ )
Bayes' Theorem	P( $B_i$ \|A) = P(A\| $B_i$ )P( $B_i$ ) / sum P(A\| $B_j$ )P( $B_j$ )
Binomial PMF	P(X=r) = C(n,r) * $p^r$ * q^(n-r)
Binomial Mean	E(X) = np
Binomial Variance	Var(X) = npq
De Morgan	P((A intersect B)') = P(A' union B')
P(at least one)	1 - P(none) = 1 - $q^n$ (independent)
P(A union B union C)	P(A)+P(B)+P(C)-P(AB)-P(BC)-P(AC)+P(ABC)