Intro to Set Theory
Set Theory, Simplified
Sets are a collection of things - numbers, pencils, toys, fans, and so on. These are denoted by a capital letter and brackets.
Within a set exists elements - the stuff inside each set.
The number of elements within a set is known as a cardinal number, denoted by the letter n.
A universal set, AKA the sample field, is the set of all numbers, given by either the symbol Ω, S, or U.
Two or more sets are considered mutually exclusive if they don’t share any of the same elements.
Unions are either this or that - the two said sets may be intersecting. Unions are denoted as (A∪B).
Intersections are and - the element must share a common event with the given sets. Intersections are denoted as (A∩B).
Compliments are not- any element that is not within the stated set. Compliments are denoted as any of the following:
Conditionals are given- the element not only must share a common event with the given sets, but the given event is assumed to be true from some point forward. Conditionals are denoted as (A|B).
Probability Rules and Assumptions
The sum of all individual probabilities shall equal 1.
Probabilities must neither be less than 0 nor be greater than 1.
Probabilities refer to what happens in the long run.
Probabilities should never "bounce" because an event doesn't happen for a long time.
Model probabilities. It will help.