Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more. 
Home Math Background Set Theorie Union and Intersection  
See also: Complementary Sets and Subsets  
Union and Intersection
Compound events are formed from several sample points belonging to different events. These operations can be described by set theory
and its operators. These operations can be nicely visualized and easily understood by using the socalled Venn diagram. The most basic operators are the union and intersection.
Example: Let us take a quick look at the game Roulette (the European version with only one zero field): How many numbers let us win, if we bet on the red numbers and the numbers of the third column? In order to evaluate this we have to calculate the union of the set A (the red numbers) and the set B (the numbers in the third column). A B contains 22 numbers, which are comprised of 18 red numbers and the 12 numbers in the third column. It is evident that the nnumber of elements of the union A B is smaller than the sum of the individual sets, since some of the numbers belong to both sets.
How many numbers win twice if we bet on red and the third column? In order to win twice the selected number has to be an element of the intersection of set A (red numbers) and set B (numbers in the third column). The insection contains 8 numbers, thus we have a chance of 8/37 to win twice.
The probabilities of compound events can be calculated by counting the sample points and applying the summation rule. In addition, there exist some rules to calculate the probabilities for more complex problems which do not allow to count the sample points.


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