Hey Developer’s, I’m back with a new topic which is Set Operations On Events in the series of statistics foundations.
Quick Referesher
Simple Event : It cannot be decomposed. Ex: Player Rolled a 6
Complex Event : It can be decomposed into simpler events. Ex: Player rolled a even number can be decomposd into player rolled a 2,4 or 6.
So, let’s get started …
Set Union
A union of two sets A and B is basically a set that contains all the elements from A and B, and the common elements do not repeat.
Ex: if A = {1,2,3} and B = {1,x,∞} then A ⋃ B = {1,2,3,x,∞}
Set Intersection
An intersection of two sets A and B is a set containing all that belong to both A and B.
Basically the common elements from both the sets.
Ex: if A = {1,2,3} and B = {1,x,∞} then A ⋂ B = {1}
Set Difference
The relative complement or set difference of sets A and B denoted A – B, is the set of all elements in A that are not in B.
Ex: If A = {1,2,3} and B = {3,4,5} then A – B = {1,2}
Set Operations On Events
Suppose a die roll is, S = {E1,E2,E3,E4,E5,E6}
An even roll is ,S(even) = {E2,E4,E6}
An roll that is greater than 3, S>3 = {E4,E5,E6}
A roll that is even or greater than 3, S(even) ∪ S>3 = {E2,E4,E5,E6}
A roll that is even and greater than 3, S(even) ∩ S>3 = {E4,E6}
A roll that is odd and greater than 5,S(odd) ∩ S>5 = ∅
Next Post will be on Independence Of Events
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