__Classical Definition__: $$P(A)=\frac{\text{# of ways event $A$ can occur}}{\text{# of outcomes in $S$}}$$
Assumption: All outcomes are equally likely.__Relative Frequency Definition__: $$P(A)=\frac{\text{# of ways event $A$ occured}}{\text{# of repetitions of experiment}}$$
Limitation: Can never repeat an experiment indefinitely or even a long series of repetitions.__Subjective Probability Definition__: The probability of an event is a measure of how sure the person making the statement is that the event would occur.
Limitation: No rational basis for agreement on a right answer.

e.g. $S=\{\text{"heads, "tails"}\}$.

- Discrete
- Takes only integer values
- Things we count
- Can be further classified as:
- Finite: e.g. rolling a die twice
- Countably Infinite: e.g. tossing a coin till a head appears
- Continuous
- Takes any real values
- Things we measure

- Simple Event: An event that consists of 1 element
- Compound Event: An event that has more than one element

- P(S)=1; P($\phi$)=0
- $P(\cup_{i=1}^\infty A_i)=\sum_{i=1}^\infty P(A_i)$, $A_i\cap A_j=\phi$ ($A_i$ and $A_j$ are "mutually exclusive" or "disjoint")

If 2 events are disjoint, then $P(A_i\cup A_j)=P(A_i)+P(A_j)$