Sample Spaces and The Algebra of Sets | Probability And Statistics Tutorial

Before being introduced to probability, you need to be familiar with Sample Spaces and the Algebra of sets. Sample Spaces is referred to the potential outcomes of an event. To understand better, consider the following examples:

What is the sample space of the experiment of flipping a coin 3 times?
Basically you are going to flip a coin three times and record outcome of each toss and the ordered triples would be your sample outcome.
Sample Space, S, = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}.

What is the sample space for choosing an even number from 0 to 10 at random?
S = {2, 4, 6, 8, 10}.
The algebra of sets is the operations Unions, Intersections, and Complements. Let A and B be any two events defined over the same sample S. The Intersection of A and B, written A ∩ B, is the event whose outcome belong to both A and B. The Union of A and B, written A ∪ B, is the event whose outcomes belong to either A or B or both. To understand the concept of Intersections and Unions, consider the following examples:

A be the set of x's for which x^2 + 2x = 8
B be the set of x's for which x^2 + 1x = 6

The solution of the events:
A = (X+4)*(X-2) = {-4,2}
B = (X+3)*(X-2) = {-2,2}
A ∩ B = {2}
A ∪ B = {-3,-2,2} 

A Complement, written A^c, of A refers to things not in A but things outside of A. To understand the concept of algebra of sets, consider the following image, which should be self-explanatory:

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