Sample Spaces and Events

We continue in statistics by talking about sample spaces and events. We cover the union of an event, the complement of an event, the intersection of an event, and tackle a problem at the end.

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[philosophyversuslogic]

For students I demonstrate this using the set theory /ST/ in a quite similar way, but I add two new operations to make those processes /union, and intersection/ easier in a formal way. Here they are:
if S is a set with two or more similar elements, let's say {1, 2, 2, 3}, there's an operation of STsimplification such as: if there's a set S, then to get S` we have to remove the similar elements and leave just one of them /for instance: {1, 2, 2, 3} = {1, 2, 3}; or {2, 2, 3, 3, 4} = {2, 3, 4}.
Another operation is reversed, called STcomplication: if there's a set S, then to get S`` we have to remove all the elements which don't have similar elements, for example: {1, 2, 2, 3} = {2, 2}, or {2, 2, 3, 3, 4} = {2, 3}.
Then the operations of union and intersection can be made by these steps /I'll simplify these steps right now/: the union of sets A {1, 2, 2, 3} and B {2, 3, 4} is to write a set C such as it adds the elements of B to the set of A via comma: {1, 2, 2, 3, 2, 3, 4}, and after that we provide an operation of STsimplification -> {1, 2, 3, 4}. Intersection requires three steps: to write the elements as in the previous example /{1, 2, 2, 3, 2, 3, 4}, then to provide an operation of STcomplication: {2, 2, 3, 3}, and at last an operation of STsimp: {2, 3}.