An event is any subset E of a sample space S.

The sample space S is the set of all possible outcomes of a random experiment.

An impossible event is represented by the empty set φ and cannot occur.

A sure event is the sample space S itself, meaning it always occurs.

A simple event contains only one outcome from the sample space.

A compound event is one that includes more than one outcome.

The complementary event A' consists of outcomes not in event A (A' = S - A).

A ∪ B represents the event 'A or B or both'.

A ∩ B signifies the event 'A and B', containing outcomes common to both.

Two events are mutually exclusive if they cannot occur together (A ∩ B = φ).

Events are exhaustive if their union equals the sample space S (E1 ∪ E2 ∪ ... = S).

P(E) is defined as the number of favorable outcomes to the total number of outcomes.

P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

P(A ∪ B) = P(A) + P(B), since A ∩ B = φ.

P(not A) = 1 - P(A).

Each outcome has the same probability of occurring; P(ωi) = 1/n.

S = {HH, HT, TH, TT}.

P(E) = m/n, where m is the number of favorable outcomes, and n is the total outcomes.