Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and here for more.

Calculating with Sets

When combining two or more sets by union or intersection, the following rules have to be applied:
Commutative Law A B = B A
Associative Law (A B) C = A (B C)
Distributive Law (A B) C = 
(A C) (B C)
De Morgan's Laws ~(A B) = ~A   ~B
~(A  B) = ~A   ~B

A visualization of the distributive law:
AuB C =
(A B) C
(A C) (B C) (A C) (B C)

Example: When we define an additional event C {number larger than 1} and calculate the union and intersection of all three events A, B and C, we find that the probability of the union equals 1 and the probability of the intersection is zero.

Event Sample points Probability
A { 2 4 6} 3*1/6
B {1 2 3} 3*1/6
C {2 3 4 5 6} 5*1/6
A B {1 2 3 4 5 6} 6*1/6
A B C {} 0*1/6

Last Update: 2012-10-08