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$$ \cup := \text{or (union)} \qquad \cap := \text{and (intersection)} \qquad | := \text{given (conditional)} $$

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Sample Space ($S$)

The sample space, denoted by $S$, refers to the set of all possible outcomes of an experiment.

Space of Events $F$

The space of events, denoted by $F$ or $P(S)$, represents the set containing all possible events that can occur in an experiment.

1. Sample Space: $S$
2. Space of Events: $F=2^S$
3. Power Set: $P(S)$

Event $E$

Any subset of the sample space representing a particular outcome or combination of outcomes.

The Law of Total Probability:

$$ P(E) = P(E \cap H_1) + ..... +P(E \cap H_n) \; Law \;of \;total \;probability $$

$$ H_i \cap H_j = \emptyset \quad \text{(Mutually Exclusive)} $$

$$ \bigcup_{i=1}^{K} H_i = S \quad \text{(Collectively Exhaustive)} $$

Axioms of Probability

Permutation:

Combination:

Conditional Probability

Independence