You are working with the text-only light edition of "H.Lohninger: Teach/Me Data Analysis, Springer-Verlag, Berlin-New York-Tokyo, 1999. ISBN 3-540-14743-8". Click here for further information.
| You are working with the text-only light edition of "H.Lohninger: Teach/Me Data Analysis, Springer-Verlag, Berlin-New York-Tokyo, 1999. ISBN 3-540-14743-8". Click here for further information.
|
Table of Contents  Math Background Introduction to Probability Calculating with Sets |
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| See also: union, intersection, complement |   |
When combining two or more sets by union or intersection, the following rules
have to be applied:
| Commutative Law | A È B = B È A |
| Associative Law | (A È B) È C = A È (B È C) |
| Distributive Law | (A È B) Ç C =
(A Ç C) È (B Ç C) |
| De Morgan's Laws |
~(A È B) = ~A Ç ~B |
A visualization of the distributive law:
 |
Ç |  |
= | |
| (A È B) | C | |||
 |
È |  |
= |  |
| (A Ç C) | (B Ç C) | (AÇ C) È (BÇ C) |
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 È BÈ C {1 2 3 4 5 6} 6*1/6 A Ç BÇ C {} 0*1/6
Last Update: 2005-Jän-25