Probability

Describing the likelihood of an Event from $[0,1]$.

• 0 Means will not happen
• 1 Means guaranteed to happen

Definitions

• Experiment
• Sample Space
• Event

Probability

The probability is the Set Cardinality of an Event divided by the Set Cardinality of the sample space. $\frac{|E|}{|S|}$

Indicator Expectation Definition

$P(A)=E(I_A)$

Concepts

• Probability Function
• Complement Probability

Likelihoods

• Equally Likely

Types of probability

• Empirical Probability
• Theoretical probability
• Conditional Probability
• Subjective probability

Probability Rules

• Probability Axioms
• Probability Sum Rule
• Complement Rule
• Inclusion-Exclusion Rule
• Law of Total Probability